Algebra Examples

$(3 - \sqrt{- 2}) \cdot \sqrt{- 72} - \sqrt{- 50} + 1$

Step 1

Simplify each term.

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Step 1.1

Rewrite $- 2$ as $- 1 (2)$ .

$(3 - \sqrt{- 1 (2)}) \cdot \sqrt{- 72} - \sqrt{- 50} + 1$

Step 1.2

Rewrite $\sqrt{- 1 (2)}$ as $\sqrt{- 1} \cdot \sqrt{2}$ .

$(3 - (\sqrt{- 1} \cdot \sqrt{2})) \cdot \sqrt{- 72} - \sqrt{- 50} + 1$

Step 1.3

Rewrite $\sqrt{- 1}$ as $i$ .

$(3 - (i \cdot \sqrt{2})) \cdot \sqrt{- 72} - \sqrt{- 50} + 1$

Step 1.4

Rewrite $- 72$ as $- 1 (72)$ .

$(3 - (i \cdot \sqrt{2})) \cdot \sqrt{- 1 (72)} - \sqrt{- 50} + 1$

Step 1.5

Rewrite $\sqrt{- 1 (72)}$ as $\sqrt{- 1} \cdot \sqrt{72}$ .

$(3 - (i \cdot \sqrt{2})) \cdot (\sqrt{- 1} \cdot \sqrt{72}) - \sqrt{- 50} + 1$

Step 1.6

Rewrite $\sqrt{- 1}$ as $i$ .

$(3 - (i \cdot \sqrt{2})) \cdot (i \cdot \sqrt{72}) - \sqrt{- 50} + 1$

Step 1.7

Remove parentheses.

$(3 - i \sqrt{2}) \cdot (i \cdot \sqrt{72}) - \sqrt{- 50} + 1$

Step 1.8

Rewrite $72$ as $6^{2} \cdot 2$ .

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Step 1.8.1

Factor $36$ out of $72$ .

$(3 - i \sqrt{2}) \cdot (i \cdot \sqrt{36 (2)}) - \sqrt{- 50} + 1$

Step 1.8.2

Rewrite $36$ as $6^{2}$ .

$(3 - i \sqrt{2}) \cdot (i \cdot \sqrt{6^{2} \cdot 2}) - \sqrt{- 50} + 1$

Step 1.9

Pull terms out from under the radical.

$(3 - i \sqrt{2}) \cdot (i \cdot (6 \sqrt{2})) - \sqrt{- 50} + 1$

Step 1.10

Move $6$ to the left of $i$ .

$(3 - i \sqrt{2}) \cdot (6 \cdot i \sqrt{2}) - \sqrt{- 50} + 1$

Step 1.11

Apply the distributive property.

$3 (6 i \sqrt{2}) - i \sqrt{2} (6 i \sqrt{2}) - \sqrt{- 50} + 1$

Step 1.12

Multiply $6$ by $3$ .

$18 (i \sqrt{2}) - i \sqrt{2} (6 i \sqrt{2}) - \sqrt{- 50} + 1$

Step 1.13

Multiply $- i \sqrt{2} (6 i \sqrt{2})$ .

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Step 1.13.1

Multiply $6$ by $- 1$ .

$18 (i \sqrt{2}) - 6 i \sqrt{2} (i \sqrt{2}) - \sqrt{- 50} + 1$

Step 1.13.2

Raise $i$ to the power of $1$ .

$18 (i \sqrt{2}) - 6 (i^{1} i) \sqrt{2} \sqrt{2} - \sqrt{- 50} + 1$

Step 1.13.3

Raise $i$ to the power of $1$ .

$18 (i \sqrt{2}) - 6 (i^{1} i^{1}) \sqrt{2} \sqrt{2} - \sqrt{- 50} + 1$

Step 1.13.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$18 (i \sqrt{2}) - 6 i^{1 + 1} \sqrt{2} \sqrt{2} - \sqrt{- 50} + 1$

Step 1.13.5

Add $1$ and $1$ .

$18 (i \sqrt{2}) - 6 i^{2} \sqrt{2} \sqrt{2} - \sqrt{- 50} + 1$

Step 1.13.6

Raise $\sqrt{2}$ to the power of $1$ .

$18 (i \sqrt{2}) - 6 i^{2} ({\sqrt{2}}^{1} \sqrt{2}) - \sqrt{- 50} + 1$

Step 1.13.7

Raise $\sqrt{2}$ to the power of $1$ .

$18 (i \sqrt{2}) - 6 i^{2} ({\sqrt{2}}^{1} {\sqrt{2}}^{1}) - \sqrt{- 50} + 1$

Step 1.13.8

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$18 (i \sqrt{2}) - 6 i^{2} {\sqrt{2}}^{1 + 1} - \sqrt{- 50} + 1$

Step 1.13.9

Add $1$ and $1$ .

$18 (i \sqrt{2}) - 6 i^{2} {\sqrt{2}}^{2} - \sqrt{- 50} + 1$

Step 1.14

Simplify each term.

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Step 1.14.1

Rewrite $i^{2}$ as $- 1$ .

$18 i \sqrt{2} - 6 \cdot - 1 {\sqrt{2}}^{2} - \sqrt{- 50} + 1$

Step 1.14.2

Multiply $- 6$ by $- 1$ .

$18 i \sqrt{2} + 6 {\sqrt{2}}^{2} - \sqrt{- 50} + 1$

Step 1.14.3

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

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Step 1.14.3.1

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

$18 i \sqrt{2} + 6 {(2^{\frac{1}{2}})}^{2} - \sqrt{- 50} + 1$

Step 1.14.3.2

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

$18 i \sqrt{2} + 6 \cdot 2^{\frac{1}{2} \cdot 2} - \sqrt{- 50} + 1$

Step 1.14.3.3

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

$18 i \sqrt{2} + 6 \cdot 2^{\frac{2}{2}} - \sqrt{- 50} + 1$

Step 1.14.3.4

Cancel the common factor of $2$ .

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Step 1.14.3.4.1

Cancel the common factor.

$18 i \sqrt{2} + 6 \cdot 2^{\frac{2}{2}} - \sqrt{- 50} + 1$

Step 1.14.3.4.2

Rewrite the expression.

$18 i \sqrt{2} + 6 \cdot 2^{1} - \sqrt{- 50} + 1$

Step 1.14.3.5

Evaluate the exponent.

$18 i \sqrt{2} + 6 \cdot 2 - \sqrt{- 50} + 1$

Step 1.14.4

Multiply $6$ by $2$ .

$18 i \sqrt{2} + 12 - \sqrt{- 50} + 1$

Step 1.15

Rewrite $- 50$ as $- 1 (50)$ .

$18 i \sqrt{2} + 12 - \sqrt{- 1 (50)} + 1$

Step 1.16

Rewrite $\sqrt{- 1 (50)}$ as $\sqrt{- 1} \cdot \sqrt{50}$ .

$18 i \sqrt{2} + 12 - (\sqrt{- 1} \cdot \sqrt{50}) + 1$

Step 1.17

Rewrite $\sqrt{- 1}$ as $i$ .

$18 i \sqrt{2} + 12 - (i \cdot \sqrt{50}) + 1$

Step 1.18

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 1.18.1

Factor $25$ out of $50$ .

$18 i \sqrt{2} + 12 - (i \cdot \sqrt{25 (2)}) + 1$

Step 1.18.2

Rewrite $25$ as $5^{2}$ .

$18 i \sqrt{2} + 12 - (i \cdot \sqrt{5^{2} \cdot 2}) + 1$

Step 1.19

Pull terms out from under the radical.

$18 i \sqrt{2} + 12 - (i \cdot (5 \sqrt{2})) + 1$

Step 1.20

Move $5$ to the left of $i$ .

$18 i \sqrt{2} + 12 - (5 \cdot i \sqrt{2}) + 1$

Step 1.21

Multiply $5$ by $- 1$ .

$18 i \sqrt{2} + 12 - 5 i \sqrt{2} + 1$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $5 i \sqrt{2}$ from $18 i \sqrt{2}$ .

$13 i \sqrt{2} + 12 + 1$

Step 2.2

Simplify the expression.

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Step 2.2.1

Add $12$ and $1$ .

$13 i \sqrt{2} + 13$

Step 2.2.2

Reorder $13 i \sqrt{2}$ and $13$ .

$13 + 13 i \sqrt{2}$