Algebra Examples

${(\frac{\sqrt{10} + \sqrt{15} + \sqrt{5}}{2 + \sqrt{6} + \sqrt{2}})}^{2}$

Step 1

Multiply $\frac{\sqrt{10} + \sqrt{15} + \sqrt{5}}{2 + \sqrt{6} + \sqrt{2}}$ by $\frac{2 + \sqrt{6} - \sqrt{2}}{2 + \sqrt{6} - \sqrt{2}}$ .

${(\frac{\sqrt{10} + \sqrt{15} + \sqrt{5}}{2 + \sqrt{6} + \sqrt{2}} \cdot \frac{2 + \sqrt{6} - \sqrt{2}}{2 + \sqrt{6} - \sqrt{2}})}^{2}$

Step 2

Multiply $\frac{\sqrt{10} + \sqrt{15} + \sqrt{5}}{2 + \sqrt{6} + \sqrt{2}}$ by $\frac{2 + \sqrt{6} - \sqrt{2}}{2 + \sqrt{6} - \sqrt{2}}$ .

${(\frac{(\sqrt{10} + \sqrt{15} + \sqrt{5}) (2 + \sqrt{6} - \sqrt{2})}{(2 + \sqrt{6} + \sqrt{2}) (2 + \sqrt{6} - \sqrt{2})})}^{2}$

Step 3

Expand the denominator using the FOIL method.

${(\frac{(\sqrt{10} + \sqrt{15} + \sqrt{5}) (2 + \sqrt{6} - \sqrt{2})}{4 + 2 \sqrt{6} - 2 \sqrt{2} + \sqrt{6} \cdot 2 + {\sqrt{6}}^{2} - \sqrt{12} + \sqrt{2} \cdot 2 + \sqrt{12} - {\sqrt{2}}^{2}})}^{2}$

Step 4

Simplify.

${(\frac{(\sqrt{10} + \sqrt{15} + \sqrt{5}) (2 + \sqrt{6} - \sqrt{2})}{8 + 4 \sqrt{6}})}^{2}$

Step 5

Multiply $\frac{(\sqrt{10} + \sqrt{15} + \sqrt{5}) (2 + \sqrt{6} - \sqrt{2})}{8 + 4 \sqrt{6}}$ by $\frac{8 - 4 \sqrt{6}}{8 - 4 \sqrt{6}}$ .

${(\frac{(\sqrt{10} + \sqrt{15} + \sqrt{5}) (2 + \sqrt{6} - \sqrt{2})}{8 + 4 \sqrt{6}} \cdot \frac{8 - 4 \sqrt{6}}{8 - 4 \sqrt{6}})}^{2}$

Step 6

Simplify terms.

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Step 6.1

Multiply $\frac{(\sqrt{10} + \sqrt{15} + \sqrt{5}) (2 + \sqrt{6} - \sqrt{2})}{8 + 4 \sqrt{6}}$ by $\frac{8 - 4 \sqrt{6}}{8 - 4 \sqrt{6}}$ .

${(\frac{(\sqrt{10} + \sqrt{15} + \sqrt{5}) (2 + \sqrt{6} - \sqrt{2}) (8 - 4 \sqrt{6})}{(8 + 4 \sqrt{6}) (8 - 4 \sqrt{6})})}^{2}$

Step 6.2

Expand the denominator using the FOIL method.

${(\frac{(\sqrt{10} + \sqrt{15} + \sqrt{5}) (2 + \sqrt{6} - \sqrt{2}) (8 - 4 \sqrt{6})}{64 - 32 \sqrt{6} + 32 \sqrt{6} - 16 {\sqrt{6}}^{2}})}^{2}$

Step 6.3

Simplify.

${(\frac{(\sqrt{10} + \sqrt{15} + \sqrt{5}) (2 + \sqrt{6} - \sqrt{2}) (8 - 4 \sqrt{6})}{- 32})}^{2}$

Step 6.4

Cancel the common factor of $8 - 4 \sqrt{6}$ and $- 32$ .

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Step 6.4.1

Factor $4$ out of $(\sqrt{10} + \sqrt{15} + \sqrt{5}) (2 + \sqrt{6} - \sqrt{2}) (8 - 4 \sqrt{6})$ .

${(\frac{4 ((\sqrt{10} + \sqrt{15} + \sqrt{5}) (2 + \sqrt{6} - \sqrt{2}) (2 - \sqrt{6}))}{- 32})}^{2}$

Step 6.4.2

Cancel the common factors.

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Step 6.4.2.1

Factor $4$ out of $- 32$ .

${(\frac{4 ((\sqrt{10} + \sqrt{15} + \sqrt{5}) (2 + \sqrt{6} - \sqrt{2}) (2 - \sqrt{6}))}{4 (- 8)})}^{2}$

Step 6.4.2.2

Cancel the common factor.

${(\frac{4 ((\sqrt{10} + \sqrt{15} + \sqrt{5}) (2 + \sqrt{6} - \sqrt{2}) (2 - \sqrt{6}))}{4 \cdot - 8})}^{2}$

Step 6.4.2.3

Rewrite the expression.

${(\frac{(\sqrt{10} + \sqrt{15} + \sqrt{5}) (2 + \sqrt{6} - \sqrt{2}) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7

Simplify the numerator.

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Step 7.1

Expand $(\sqrt{10} + \sqrt{15} + \sqrt{5}) (2 + \sqrt{6} - \sqrt{2})$ by multiplying each term in the first expression by each term in the second expression.

${(\frac{(\sqrt{10} \cdot 2 + \sqrt{10} \sqrt{6} + \sqrt{10} (- \sqrt{2}) + \sqrt{15} \cdot 2 + \sqrt{15} \sqrt{6} + \sqrt{15} (- \sqrt{2}) + \sqrt{5} \cdot 2 + \sqrt{5} \sqrt{6} + \sqrt{5} (- \sqrt{2})) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.2

Move $2$ to the left of $\sqrt{10}$ .

${(\frac{(2 \cdot \sqrt{10} + \sqrt{10} \sqrt{6} + \sqrt{10} (- \sqrt{2}) + \sqrt{15} \cdot 2 + \sqrt{15} \sqrt{6} + \sqrt{15} (- \sqrt{2}) + \sqrt{5} \cdot 2 + \sqrt{5} \sqrt{6} + \sqrt{5} (- \sqrt{2})) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.3

Combine using the product rule for radicals.

${(\frac{(2 \sqrt{10} + \sqrt{10 \cdot 6} + \sqrt{10} (- \sqrt{2}) + \sqrt{15} \cdot 2 + \sqrt{15} \sqrt{6} + \sqrt{15} (- \sqrt{2}) + \sqrt{5} \cdot 2 + \sqrt{5} \sqrt{6} + \sqrt{5} (- \sqrt{2})) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.4

Multiply $10$ by $6$ .

${(\frac{(2 \sqrt{10} + \sqrt{60} + \sqrt{10} (- \sqrt{2}) + \sqrt{15} \cdot 2 + \sqrt{15} \sqrt{6} + \sqrt{15} (- \sqrt{2}) + \sqrt{5} \cdot 2 + \sqrt{5} \sqrt{6} + \sqrt{5} (- \sqrt{2})) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.5

Multiply $\sqrt{10} (- \sqrt{2})$ .

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Step 7.5.1

Combine using the product rule for radicals.

${(\frac{(2 \sqrt{10} + \sqrt{60} - \sqrt{10 \cdot 2} + \sqrt{15} \cdot 2 + \sqrt{15} \sqrt{6} + \sqrt{15} (- \sqrt{2}) + \sqrt{5} \cdot 2 + \sqrt{5} \sqrt{6} + \sqrt{5} (- \sqrt{2})) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.5.2

Multiply $10$ by $2$ .

${(\frac{(2 \sqrt{10} + \sqrt{60} - \sqrt{20} + \sqrt{15} \cdot 2 + \sqrt{15} \sqrt{6} + \sqrt{15} (- \sqrt{2}) + \sqrt{5} \cdot 2 + \sqrt{5} \sqrt{6} + \sqrt{5} (- \sqrt{2})) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.6

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 7.6.1

Factor $4$ out of $20$ .

${(\frac{(2 \sqrt{10} + \sqrt{60} - \sqrt{4 (5)} + \sqrt{15} \cdot 2 + \sqrt{15} \sqrt{6} + \sqrt{15} (- \sqrt{2}) + \sqrt{5} \cdot 2 + \sqrt{5} \sqrt{6} + \sqrt{5} (- \sqrt{2})) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.6.2

Rewrite $4$ as $2^{2}$ .

${(\frac{(2 \sqrt{10} + \sqrt{60} - \sqrt{2^{2} \cdot 5} + \sqrt{15} \cdot 2 + \sqrt{15} \sqrt{6} + \sqrt{15} (- \sqrt{2}) + \sqrt{5} \cdot 2 + \sqrt{5} \sqrt{6} + \sqrt{5} (- \sqrt{2})) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.7

Pull terms out from under the radical.

${(\frac{(2 \sqrt{10} + \sqrt{60} - (2 \sqrt{5}) + \sqrt{15} \cdot 2 + \sqrt{15} \sqrt{6} + \sqrt{15} (- \sqrt{2}) + \sqrt{5} \cdot 2 + \sqrt{5} \sqrt{6} + \sqrt{5} (- \sqrt{2})) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.8

Multiply $2$ by $- 1$ .

${(\frac{(2 \sqrt{10} + \sqrt{60} - 2 \sqrt{5} + \sqrt{15} \cdot 2 + \sqrt{15} \sqrt{6} + \sqrt{15} (- \sqrt{2}) + \sqrt{5} \cdot 2 + \sqrt{5} \sqrt{6} + \sqrt{5} (- \sqrt{2})) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.9

Move $2$ to the left of $\sqrt{15}$ .

${(\frac{(2 \sqrt{10} + \sqrt{60} - 2 \sqrt{5} + 2 \cdot \sqrt{15} + \sqrt{15} \sqrt{6} + \sqrt{15} (- \sqrt{2}) + \sqrt{5} \cdot 2 + \sqrt{5} \sqrt{6} + \sqrt{5} (- \sqrt{2})) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.10

Combine using the product rule for radicals.

${(\frac{(2 \sqrt{10} + \sqrt{60} - 2 \sqrt{5} + 2 \sqrt{15} + \sqrt{15 \cdot 6} + \sqrt{15} (- \sqrt{2}) + \sqrt{5} \cdot 2 + \sqrt{5} \sqrt{6} + \sqrt{5} (- \sqrt{2})) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.11

Multiply $15$ by $6$ .

${(\frac{(2 \sqrt{10} + \sqrt{60} - 2 \sqrt{5} + 2 \sqrt{15} + \sqrt{90} + \sqrt{15} (- \sqrt{2}) + \sqrt{5} \cdot 2 + \sqrt{5} \sqrt{6} + \sqrt{5} (- \sqrt{2})) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.12

Multiply $\sqrt{15} (- \sqrt{2})$ .

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Step 7.12.1

Combine using the product rule for radicals.

${(\frac{(2 \sqrt{10} + \sqrt{60} - 2 \sqrt{5} + 2 \sqrt{15} + \sqrt{90} - \sqrt{15 \cdot 2} + \sqrt{5} \cdot 2 + \sqrt{5} \sqrt{6} + \sqrt{5} (- \sqrt{2})) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.12.2

Multiply $15$ by $2$ .

${(\frac{(2 \sqrt{10} + \sqrt{60} - 2 \sqrt{5} + 2 \sqrt{15} + \sqrt{90} - \sqrt{30} + \sqrt{5} \cdot 2 + \sqrt{5} \sqrt{6} + \sqrt{5} (- \sqrt{2})) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.13

Move $2$ to the left of $\sqrt{5}$ .

${(\frac{(2 \sqrt{10} + \sqrt{60} - 2 \sqrt{5} + 2 \sqrt{15} + \sqrt{90} - \sqrt{30} + 2 \cdot \sqrt{5} + \sqrt{5} \sqrt{6} + \sqrt{5} (- \sqrt{2})) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.14

Combine using the product rule for radicals.

${(\frac{(2 \sqrt{10} + \sqrt{60} - 2 \sqrt{5} + 2 \sqrt{15} + \sqrt{90} - \sqrt{30} + 2 \sqrt{5} + \sqrt{5 \cdot 6} + \sqrt{5} (- \sqrt{2})) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.15

Multiply $5$ by $6$ .

${(\frac{(2 \sqrt{10} + \sqrt{60} - 2 \sqrt{5} + 2 \sqrt{15} + \sqrt{90} - \sqrt{30} + 2 \sqrt{5} + \sqrt{30} + \sqrt{5} (- \sqrt{2})) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.16

Multiply $\sqrt{5} (- \sqrt{2})$ .

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Step 7.16.1

Combine using the product rule for radicals.

${(\frac{(2 \sqrt{10} + \sqrt{60} - 2 \sqrt{5} + 2 \sqrt{15} + \sqrt{90} - \sqrt{30} + 2 \sqrt{5} + \sqrt{30} - \sqrt{5 \cdot 2}) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.16.2

Multiply $5$ by $2$ .

${(\frac{(2 \sqrt{10} + \sqrt{60} - 2 \sqrt{5} + 2 \sqrt{15} + \sqrt{90} - \sqrt{30} + 2 \sqrt{5} + \sqrt{30} - \sqrt{10}) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.17

Simplify each term.

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Step 7.17.1

Rewrite $60$ as $2^{2} \cdot 15$ .

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Step 7.17.1.1

Factor $4$ out of $60$ .

${(\frac{(2 \sqrt{10} + \sqrt{4 (15)} - 2 \sqrt{5} + 2 \sqrt{15} + \sqrt{90} - \sqrt{30} + 2 \sqrt{5} + \sqrt{30} - \sqrt{10}) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.17.1.2

Rewrite $4$ as $2^{2}$ .

${(\frac{(2 \sqrt{10} + \sqrt{2^{2} \cdot 15} - 2 \sqrt{5} + 2 \sqrt{15} + \sqrt{90} - \sqrt{30} + 2 \sqrt{5} + \sqrt{30} - \sqrt{10}) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.17.2

Pull terms out from under the radical.

${(\frac{(2 \sqrt{10} + 2 \sqrt{15} - 2 \sqrt{5} + 2 \sqrt{15} + \sqrt{90} - \sqrt{30} + 2 \sqrt{5} + \sqrt{30} - \sqrt{10}) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.17.3

Rewrite $90$ as $3^{2} \cdot 10$ .

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Step 7.17.3.1

Factor $9$ out of $90$ .

${(\frac{(2 \sqrt{10} + 2 \sqrt{15} - 2 \sqrt{5} + 2 \sqrt{15} + \sqrt{9 (10)} - \sqrt{30} + 2 \sqrt{5} + \sqrt{30} - \sqrt{10}) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.17.3.2

Rewrite $9$ as $3^{2}$ .

${(\frac{(2 \sqrt{10} + 2 \sqrt{15} - 2 \sqrt{5} + 2 \sqrt{15} + \sqrt{3^{2} \cdot 10} - \sqrt{30} + 2 \sqrt{5} + \sqrt{30} - \sqrt{10}) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.17.4

Pull terms out from under the radical.

${(\frac{(2 \sqrt{10} + 2 \sqrt{15} - 2 \sqrt{5} + 2 \sqrt{15} + 3 \sqrt{10} - \sqrt{30} + 2 \sqrt{5} + \sqrt{30} - \sqrt{10}) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.18

Add $2 \sqrt{10}$ and $3 \sqrt{10}$ .

${(\frac{(5 \sqrt{10} + 2 \sqrt{15} - 2 \sqrt{5} + 2 \sqrt{15} - \sqrt{30} + 2 \sqrt{5} + \sqrt{30} - \sqrt{10}) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.19

Subtract $\sqrt{10}$ from $5 \sqrt{10}$ .

${(\frac{(4 \sqrt{10} + 2 \sqrt{15} - 2 \sqrt{5} + 2 \sqrt{15} - \sqrt{30} + 2 \sqrt{5} + \sqrt{30}) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.20

Add $2 \sqrt{15}$ and $2 \sqrt{15}$ .

${(\frac{(4 \sqrt{10} + 4 \sqrt{15} - 2 \sqrt{5} - \sqrt{30} + 2 \sqrt{5} + \sqrt{30}) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.21

Add $- 2 \sqrt{5}$ and $2 \sqrt{5}$ .

${(\frac{(4 \sqrt{10} + 4 \sqrt{15} + 0 - \sqrt{30} + \sqrt{30}) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.22

Add $4 \sqrt{10}$ and $0$ .

${(\frac{(4 \sqrt{10} + 4 \sqrt{15} - \sqrt{30} + \sqrt{30}) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.23

Add $- \sqrt{30}$ and $\sqrt{30}$ .

${(\frac{(4 \sqrt{10} + 4 \sqrt{15} + 0) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.24

Add $4 \sqrt{10}$ and $0$ .

${(\frac{(4 \sqrt{10} + 4 \sqrt{15}) (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.25

Expand $(4 \sqrt{10} + 4 \sqrt{15}) (2 - \sqrt{6})$ using the FOIL Method.

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Step 7.25.1

Apply the distributive property.

${(\frac{4 \sqrt{10} (2 - \sqrt{6}) + 4 \sqrt{15} (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.25.2

Apply the distributive property.

${(\frac{4 \sqrt{10} \cdot 2 + 4 \sqrt{10} (- \sqrt{6}) + 4 \sqrt{15} (2 - \sqrt{6})}{- 8})}^{2}$

Step 7.25.3

Apply the distributive property.

${(\frac{4 \sqrt{10} \cdot 2 + 4 \sqrt{10} (- \sqrt{6}) + 4 \sqrt{15} \cdot 2 + 4 \sqrt{15} (- \sqrt{6})}{- 8})}^{2}$

Step 7.26

Simplify and combine like terms.

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Step 7.26.1

Simplify each term.

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Step 7.26.1.1

Multiply $2$ by $4$ .

${(\frac{8 \sqrt{10} + 4 \sqrt{10} (- \sqrt{6}) + 4 \sqrt{15} \cdot 2 + 4 \sqrt{15} (- \sqrt{6})}{- 8})}^{2}$

Step 7.26.1.2

Multiply $4 \sqrt{10} (- \sqrt{6})$ .

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Step 7.26.1.2.1

Multiply $- 1$ by $4$ .

${(\frac{8 \sqrt{10} - 4 \sqrt{10} \sqrt{6} + 4 \sqrt{15} \cdot 2 + 4 \sqrt{15} (- \sqrt{6})}{- 8})}^{2}$

Step 7.26.1.2.2

Combine using the product rule for radicals.

${(\frac{8 \sqrt{10} - 4 \sqrt{6 \cdot 10} + 4 \sqrt{15} \cdot 2 + 4 \sqrt{15} (- \sqrt{6})}{- 8})}^{2}$

Step 7.26.1.2.3

Multiply $6$ by $10$ .

${(\frac{8 \sqrt{10} - 4 \sqrt{60} + 4 \sqrt{15} \cdot 2 + 4 \sqrt{15} (- \sqrt{6})}{- 8})}^{2}$

Step 7.26.1.3

Rewrite $60$ as $2^{2} \cdot 15$ .

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Step 7.26.1.3.1

Factor $4$ out of $60$ .

${(\frac{8 \sqrt{10} - 4 \sqrt{4 (15)} + 4 \sqrt{15} \cdot 2 + 4 \sqrt{15} (- \sqrt{6})}{- 8})}^{2}$

Step 7.26.1.3.2

Rewrite $4$ as $2^{2}$ .

${(\frac{8 \sqrt{10} - 4 \sqrt{2^{2} \cdot 15} + 4 \sqrt{15} \cdot 2 + 4 \sqrt{15} (- \sqrt{6})}{- 8})}^{2}$

Step 7.26.1.4

Pull terms out from under the radical.

${(\frac{8 \sqrt{10} - 4 (2 \sqrt{15}) + 4 \sqrt{15} \cdot 2 + 4 \sqrt{15} (- \sqrt{6})}{- 8})}^{2}$

Step 7.26.1.5

Multiply $2$ by $- 4$ .

${(\frac{8 \sqrt{10} - 8 \sqrt{15} + 4 \sqrt{15} \cdot 2 + 4 \sqrt{15} (- \sqrt{6})}{- 8})}^{2}$

Step 7.26.1.6

Multiply $2$ by $4$ .

${(\frac{8 \sqrt{10} - 8 \sqrt{15} + 8 \sqrt{15} + 4 \sqrt{15} (- \sqrt{6})}{- 8})}^{2}$

Step 7.26.1.7

Multiply $4 \sqrt{15} (- \sqrt{6})$ .

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Step 7.26.1.7.1

Multiply $- 1$ by $4$ .

${(\frac{8 \sqrt{10} - 8 \sqrt{15} + 8 \sqrt{15} - 4 \sqrt{15} \sqrt{6}}{- 8})}^{2}$

Step 7.26.1.7.2

Combine using the product rule for radicals.

${(\frac{8 \sqrt{10} - 8 \sqrt{15} + 8 \sqrt{15} - 4 \sqrt{6 \cdot 15}}{- 8})}^{2}$

Step 7.26.1.7.3

Multiply $6$ by $15$ .

${(\frac{8 \sqrt{10} - 8 \sqrt{15} + 8 \sqrt{15} - 4 \sqrt{90}}{- 8})}^{2}$

Step 7.26.1.8

Rewrite $90$ as $3^{2} \cdot 10$ .

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Step 7.26.1.8.1

Factor $9$ out of $90$ .

${(\frac{8 \sqrt{10} - 8 \sqrt{15} + 8 \sqrt{15} - 4 \sqrt{9 (10)}}{- 8})}^{2}$

Step 7.26.1.8.2

Rewrite $9$ as $3^{2}$ .

${(\frac{8 \sqrt{10} - 8 \sqrt{15} + 8 \sqrt{15} - 4 \sqrt{3^{2} \cdot 10}}{- 8})}^{2}$

Step 7.26.1.9

Pull terms out from under the radical.

${(\frac{8 \sqrt{10} - 8 \sqrt{15} + 8 \sqrt{15} - 4 (3 \sqrt{10})}{- 8})}^{2}$

Step 7.26.1.10

Multiply $3$ by $- 4$ .

${(\frac{8 \sqrt{10} - 8 \sqrt{15} + 8 \sqrt{15} - 12 \sqrt{10}}{- 8})}^{2}$

Step 7.26.2

Subtract $12 \sqrt{10}$ from $8 \sqrt{10}$ .

${(\frac{- 4 \sqrt{10} - 8 \sqrt{15} + 8 \sqrt{15}}{- 8})}^{2}$

Step 7.26.3

Add $- 8 \sqrt{15}$ and $8 \sqrt{15}$ .

${(\frac{- 4 \sqrt{10} + 0}{- 8})}^{2}$

Step 7.26.4

Add $- 4 \sqrt{10}$ and $0$ .

${(\frac{- 4 \sqrt{10}}{- 8})}^{2}$

Step 8

Simplify terms.

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Step 8.1

Cancel the common factor of $- 4$ and $- 8$ .

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Step 8.1.1

Factor $- 4$ out of $- 4 \sqrt{10}$ .

${(\frac{- 4 (\sqrt{10})}{- 8})}^{2}$

Step 8.1.2

Cancel the common factors.

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Step 8.1.2.1

Factor $- 4$ out of $- 8$ .

${(\frac{- 4 (\sqrt{10})}{- 4 (2)})}^{2}$

Step 8.1.2.2

Cancel the common factor.

${(\frac{- 4 \sqrt{10}}{- 4 \cdot 2})}^{2}$

Step 8.1.2.3

Rewrite the expression.

${(\frac{\sqrt{10}}{2})}^{2}$

Step 8.2

Apply the product rule to $\frac{\sqrt{10}}{2}$ .

$\frac{{\sqrt{10}}^{2}}{2^{2}}$

Step 8.3

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

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Step 8.3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$\frac{{(10^{\frac{1}{2}})}^{2}}{2^{2}}$

Step 8.3.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{10^{\frac{1}{2} \cdot 2}}{2^{2}}$

Step 8.3.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{10^{\frac{2}{2}}}{2^{2}}$

Step 8.3.4

Cancel the common factor of $2$ .

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Step 8.3.4.1

Cancel the common factor.

$\frac{10^{\frac{2}{2}}}{2^{2}}$

Step 8.3.4.2

Rewrite the expression.

$\frac{10^{1}}{2^{2}}$

Step 8.3.5

Evaluate the exponent.

$\frac{10}{2^{2}}$

Step 8.4

Raise $2$ to the power of $2$ .

$\frac{10}{4}$

Step 8.5

Cancel the common factor of $10$ and $4$ .

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Step 8.5.1

Factor $2$ out of $10$ .

$\frac{2 (5)}{4}$

Step 8.5.2

Cancel the common factors.

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Step 8.5.2.1

Factor $2$ out of $4$ .

$\frac{2 \cdot 5}{2 \cdot 2}$

Step 8.5.2.2

Cancel the common factor.

$\frac{2 \cdot 5}{2 \cdot 2}$

Step 8.5.2.3

Rewrite the expression.

$\frac{5}{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{2}$

Decimal Form:

$2.5$

Mixed Number Form:

$2 \frac{1}{2}$