Basic Math Examples

$(\sqrt{6 y}) (\sqrt[4]{36 y^{2}})$

Step 1

Rewrite $36 y^{2}$ as ${(6 y)}^{2}$ .

$\sqrt{6 y} \sqrt[4]{{(6 y)}^{2}}$

Step 2

Rewrite $\sqrt[4]{{(6 y)}^{2}}$ as $\sqrt{\sqrt{{(6 y)}^{2}}}$ .

$\sqrt{6 y} \sqrt{\sqrt{{(6 y)}^{2}}}$

Step 3

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt{6 y} \sqrt{6 y}$

Step 4

Multiply $\sqrt{6 y} \sqrt{6 y}$ .

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Step 4.1

Raise $\sqrt{6 y}$ to the power of $1$ .

${\sqrt{6 y}}^{1} \sqrt{6 y}$

Step 4.2

Raise $\sqrt{6 y}$ to the power of $1$ .

${\sqrt{6 y}}^{1} {\sqrt{6 y}}^{1}$

Step 4.3

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

${\sqrt{6 y}}^{1 + 1}$

Step 4.4

Add $1$ and $1$ .

${\sqrt{6 y}}^{2}$

Step 5

Rewrite ${\sqrt{6 y}}^{2}$ as $6 y$ .

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Step 5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6 y}$ as ${(6 y)}^{\frac{1}{2}}$ .

${({(6 y)}^{\frac{1}{2}})}^{2}$

Step 5.2

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

${(6 y)}^{\frac{1}{2} \cdot 2}$

Step 5.3

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

${(6 y)}^{\frac{2}{2}}$

Step 5.4

Cancel the common factor of $2$ .

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Step 5.4.1

Cancel the common factor.

${(6 y)}^{\frac{2}{2}}$

Step 5.4.2

Rewrite the expression.

${(6 y)}^{1}$

Step 5.5

Simplify.

$6 y$