Algebra Examples

$7 \sqrt{3 y z} \cdot 4 \sqrt{24 y z}$

Step 1

Rewrite $24 y z$ as $2^{2} \cdot (6 y z)$ .

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Step 1.1

Factor $4$ out of $24$ .

$7 \sqrt{3 y z} \cdot (4 \sqrt{4 (6) y z})$

Step 1.2

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

$7 \sqrt{3 y z} \cdot (4 \sqrt{2^{2} \cdot 6 y z})$

Step 1.3

Add parentheses.

$7 \sqrt{3 y z} \cdot (4 \sqrt{2^{2} \cdot 6 (y z)})$

Step 1.4

Add parentheses.

$7 \sqrt{3 y z} \cdot (4 \sqrt{2^{2} \cdot (6 y z)})$

Step 2

Pull terms out from under the radical.

$7 \sqrt{3 y z} \cdot (4 (2 \sqrt{6 y z}))$

Step 3

Multiply $2$ by $4$ .

$7 \sqrt{3 y z} \cdot (8 \sqrt{6 y z})$

Step 4

Multiply $7 \sqrt{3 y z} (8 \sqrt{6 y z})$ .

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Step 4.1

Multiply $8$ by $7$ .

$56 \sqrt{3 y z} \sqrt{6 y z}$

Step 4.2

Combine using the product rule for radicals.

$56 \sqrt{6 y z (3 y z)}$

Step 4.3

Multiply $3$ by $6$ .

$56 \sqrt{18 y z (y z)}$

Step 4.4

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

$56 \sqrt{18 (y^{1} y) z \cdot z}$

Step 4.5

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

$56 \sqrt{18 (y^{1} y^{1}) z \cdot z}$

Step 4.6

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

$56 \sqrt{18 y^{1 + 1} z \cdot z}$

Step 4.7

Add $1$ and $1$ .

$56 \sqrt{18 y^{2} z \cdot z}$

Step 4.8

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

$56 \sqrt{18 y^{2} (z^{1} z)}$

Step 4.9

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

$56 \sqrt{18 y^{2} (z^{1} z^{1})}$

Step 4.10

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

$56 \sqrt{18 y^{2} z^{1 + 1}}$

Step 4.11

Add $1$ and $1$ .

$56 \sqrt{18 y^{2} z^{2}}$

Step 5

Rewrite $18 y^{2} z^{2}$ as ${(3 y z)}^{2} \cdot 2$ .

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Step 5.1

Factor $9$ out of $18$ .

$56 \sqrt{9 (2) y^{2} z^{2}}$

Step 5.2

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

$56 \sqrt{3^{2} \cdot 2 y^{2} z^{2}}$

Step 5.3

Move $2$ .

$56 \sqrt{3^{2} y^{2} z^{2} \cdot 2}$

Step 5.4

Rewrite $3^{2} y^{2} z^{2}$ as ${(3 y z)}^{2}$ .

$56 \sqrt{{(3 y z)}^{2} \cdot 2}$

Step 6

Pull terms out from under the radical.

$56 (3 y z \sqrt{2})$

Step 7

Multiply $3$ by $56$ .

$168 y z \sqrt{2}$