Basic Math Examples

$\sqrt{5 w^{2} x^{3}} \sqrt{20 w^{7} x^{9}}$

Step 1

Rewrite $5 w^{2} x^{3}$ as ${(w x)}^{2} \cdot (5 x)$ .

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Step 1.1

Factor out $x^{2}$ .

$\sqrt{5 w^{2} (x^{2} x)} \sqrt{20 w^{7} x^{9}}$

Step 1.2

Move $5$ .

$\sqrt{w^{2} x^{2} \cdot 5 x} \sqrt{20 w^{7} x^{9}}$

Step 1.3

Rewrite $w^{2} x^{2}$ as ${(w x)}^{2}$ .

$\sqrt{{(w x)}^{2} \cdot 5 x} \sqrt{20 w^{7} x^{9}}$

Step 1.4

Add parentheses.

$\sqrt{{(w x)}^{2} \cdot (5 x)} \sqrt{20 w^{7} x^{9}}$

Step 2

Pull terms out from under the radical.

$w x \sqrt{5 x} \sqrt{20 w^{7} x^{9}}$

Step 3

Rewrite $20 w^{7} x^{9}$ as ${(2 w^{3} x^{4})}^{2} \cdot (5 w x)$ .

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Step 3.1

Factor $4$ out of $20$ .

$w x \sqrt{5 x} \sqrt{4 (5) w^{7} x^{9}}$

Step 3.2

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

$w x \sqrt{5 x} \sqrt{2^{2} \cdot 5 w^{7} x^{9}}$

Step 3.3

Factor out $w^{6}$ .

$w x \sqrt{5 x} \sqrt{2^{2} \cdot 5 (w^{6} w) x^{9}}$

Step 3.4

Rewrite $w^{6}$ as ${(w^{3})}^{2}$ .

$w x \sqrt{5 x} \sqrt{2^{2} \cdot 5 ({(w^{3})}^{2} w) x^{9}}$

Step 3.5

Factor out $x^{8}$ .

$w x \sqrt{5 x} \sqrt{2^{2} \cdot 5 ({(w^{3})}^{2} w) (x^{8} x)}$

Step 3.6

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

$w x \sqrt{5 x} \sqrt{2^{2} \cdot 5 ({(w^{3})}^{2} w) ({(x^{4})}^{2} x)}$

Step 3.7

Move $w$ .

$w x \sqrt{5 x} \sqrt{2^{2} \cdot 5 ({(w^{3})}^{2}) {(x^{4})}^{2} w x}$

Step 3.8

Move $5$ .

$w x \sqrt{5 x} \sqrt{(2^{2} ({(w^{3})}^{2})) {(x^{4})}^{2} \cdot 5 w x}$

Step 3.9

Rewrite $(2^{2} ({(w^{3})}^{2})) {(x^{4})}^{2}$ as ${(2 w^{3} x^{4})}^{2}$ .

$w x \sqrt{5 x} \sqrt{{(2 w^{3} x^{4})}^{2} \cdot 5 w x}$

Step 3.10

Add parentheses.

$w x \sqrt{5 x} \sqrt{{(2 w^{3} x^{4})}^{2} \cdot 5 (w x)}$

Step 3.11

Add parentheses.

$w x \sqrt{5 x} \sqrt{{(2 w^{3} x^{4})}^{2} \cdot (5 w x)}$

Step 4

Pull terms out from under the radical.

$w x \sqrt{5 x} (2 w^{3} x^{4} \sqrt{5 w x})$

Step 5

Rewrite using the commutative property of multiplication.

$2 w x \sqrt{5 x} (w^{3} x^{4} \sqrt{5 w x})$

Step 6

Multiply $w$ by $w^{3}$ by adding the exponents.

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Step 6.1

Move $w^{3}$ .

$2 (w^{3} w) x \sqrt{5 x} (x^{4} \sqrt{5 w x})$

Step 6.2

Multiply $w^{3}$ by $w$ .

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Step 6.2.1

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

$2 (w^{3} w^{1}) x \sqrt{5 x} (x^{4} \sqrt{5 w x})$

Step 6.2.2

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

$2 w^{3 + 1} x \sqrt{5 x} (x^{4} \sqrt{5 w x})$

Step 6.3

Add $3$ and $1$ .

$2 w^{4} x \sqrt{5 x} (x^{4} \sqrt{5 w x})$

Step 7

Multiply $x$ by $x^{4}$ by adding the exponents.

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Step 7.1

Move $x^{4}$ .

$2 w^{4} (x^{4} x) \sqrt{5 x} \sqrt{5 w x}$

Step 7.2

Multiply $x^{4}$ by $x$ .

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Step 7.2.1

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

$2 w^{4} (x^{4} x^{1}) \sqrt{5 x} \sqrt{5 w x}$

Step 7.2.2

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

$2 w^{4} x^{4 + 1} \sqrt{5 x} \sqrt{5 w x}$

Step 7.3

Add $4$ and $1$ .

$2 w^{4} x^{5} \sqrt{5 x} \sqrt{5 w x}$

Step 8

Multiply $2 w^{4} x^{5} \sqrt{5 x} \sqrt{5 w x}$ .

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Step 8.1

Combine using the product rule for radicals.

$2 w^{4} x^{5} \sqrt{5 w x (5 x)}$

Step 8.2

Multiply $5$ by $5$ .

$2 w^{4} x^{5} \sqrt{25 w x \cdot x}$

Step 8.3

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

$2 w^{4} x^{5} \sqrt{25 w (x^{1} x)}$

Step 8.4

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

$2 w^{4} x^{5} \sqrt{25 w (x^{1} x^{1})}$

Step 8.5

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

$2 w^{4} x^{5} \sqrt{25 w x^{1 + 1}}$

Step 8.6

Add $1$ and $1$ .

$2 w^{4} x^{5} \sqrt{25 w x^{2}}$

Step 9

Rewrite $25 w x^{2}$ as ${(5 x)}^{2} w$ .

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Step 9.1

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

$2 w^{4} x^{5} \sqrt{5^{2} w x^{2}}$

Step 9.2

Move $w$ .

$2 w^{4} x^{5} \sqrt{5^{2} x^{2} w}$

Step 9.3

Rewrite $5^{2} x^{2}$ as ${(5 x)}^{2}$ .

$2 w^{4} x^{5} \sqrt{{(5 x)}^{2} w}$

Step 10

Pull terms out from under the radical.

$2 w^{4} x^{5} (5 x \sqrt{w})$

Step 11

Multiply $x^{5}$ by $x$ by adding the exponents.

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Step 11.1

Move $x$ .

$2 w^{4} (x \cdot x^{5}) (5 \sqrt{w})$

Step 11.2

Multiply $x$ by $x^{5}$ .

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Step 11.2.1

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

$2 w^{4} (x^{1} x^{5}) (5 \sqrt{w})$

Step 11.2.2

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

$2 w^{4} x^{1 + 5} (5 \sqrt{w})$

Step 11.3

Add $1$ and $5$ .

$2 w^{4} x^{6} (5 \sqrt{w})$

Step 12

Multiply $5$ by $2$ .

$10 w^{4} x^{6} \sqrt{w}$