Basic Math Examples

$\sqrt{3 w y^{8}} \sqrt{15 w^{4} y^{3}}$

Step 1

Rewrite $3 w y^{8}$ as ${({(y^{2})}^{2})}^{2} \cdot (3 w)$ .

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Step 1.1

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

$\sqrt{3 w {(y^{4})}^{2}} \sqrt{15 w^{4} y^{3}}$

Step 1.2

Move $w$ .

$\sqrt{3 {(y^{4})}^{2} w} \sqrt{15 w^{4} y^{3}}$

Step 1.3

Reorder $3$ and ${(y^{4})}^{2}$ .

$\sqrt{{(y^{4})}^{2} \cdot 3 w} \sqrt{15 w^{4} y^{3}}$

Step 1.4

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

$\sqrt{{({(y^{2})}^{2})}^{2} \cdot 3 w} \sqrt{15 w^{4} y^{3}}$

Step 1.5

Add parentheses.

$\sqrt{{({(y^{2})}^{2})}^{2} \cdot (3 w)} \sqrt{15 w^{4} y^{3}}$

Step 2

Pull terms out from under the radical.

${(y^{2})}^{2} \sqrt{3 w} \sqrt{15 w^{4} y^{3}}$

Step 3

Multiply the exponents in ${(y^{2})}^{2}$ .

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Step 3.1

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

$y^{2 \cdot 2} \sqrt{3 w} \sqrt{15 w^{4} y^{3}}$

Step 3.2

Multiply $2$ by $2$ .

$y^{4} \sqrt{3 w} \sqrt{15 w^{4} y^{3}}$

Step 4

Rewrite $15 w^{4} y^{3}$ as ${(w^{2} y)}^{2} \cdot (15 y)$ .

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Step 4.1

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

$y^{4} \sqrt{3 w} \sqrt{15 {(w^{2})}^{2} y^{3}}$

Step 4.2

Factor out $y^{2}$ .

$y^{4} \sqrt{3 w} \sqrt{15 {(w^{2})}^{2} (y^{2} y)}$

Step 4.3

Move $15$ .

$y^{4} \sqrt{3 w} \sqrt{{(w^{2})}^{2} y^{2} \cdot 15 y}$

Step 4.4

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

$y^{4} \sqrt{3 w} \sqrt{{(w^{2} y)}^{2} \cdot 15 y}$

Step 4.5

Add parentheses.

$y^{4} \sqrt{3 w} \sqrt{{(w^{2} y)}^{2} \cdot (15 y)}$

Step 5

Pull terms out from under the radical.

$y^{4} \sqrt{3 w} (w^{2} y \sqrt{15 y})$

Step 6

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

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Step 6.1

Move $y$ .

$y \cdot y^{4} \sqrt{3 w} (w^{2} \sqrt{15 y})$

Step 6.2

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

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Step 6.2.1

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

$y^{1} y^{4} \sqrt{3 w} (w^{2} \sqrt{15 y})$

Step 6.2.2

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

$y^{1 + 4} \sqrt{3 w} (w^{2} \sqrt{15 y})$

Step 6.3

Add $1$ and $4$ .

$y^{5} \sqrt{3 w} (w^{2} \sqrt{15 y})$

Step 7

Multiply $y^{5} \sqrt{3 w} (w^{2} \sqrt{15 y})$ .

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Step 7.1

Combine using the product rule for radicals.

$y^{5} (w^{2} \sqrt{3 w (15 y)})$

Step 7.2

Multiply $15$ by $3$ .

$y^{5} (w^{2} \sqrt{45 w y})$

Step 8

Rewrite $45 w y$ as $3^{2} \cdot (5 w y)$ .

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Step 8.1

Factor $9$ out of $45$ .

$y^{5} (w^{2} \sqrt{9 (5) w y})$

Step 8.2

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

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

Step 8.3

Add parentheses.

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

Step 8.4

Add parentheses.

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

Step 9

Pull terms out from under the radical.

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

Step 10

Rewrite using the commutative property of multiplication.

$3 y^{5} w^{2} \sqrt{5 w y}$