Simplify square root of (7x)/(6y^7)

$\sqrt{\frac{7 x}{6 y^{7}}}$

Step 1

Rewrite $\frac{7 x}{6 y^{7}}$ as ${(\frac{1}{y^{3}})}^{2} \frac{7 x}{6 y}$ .

Factor the perfect power $1^{2}$ out of $7 x$ .

$\sqrt{\frac{1^{2} (7 x)}{6 y^{7}}}$

Factor the perfect power ${(y^{3})}^{2}$ out of $6 y^{7}$ .

$\sqrt{\frac{1^{2} (7 x)}{{(y^{3})}^{2} \cdot (6 y)}}$

Rearrange the fraction $\frac{1^{2} (7 x)}{{(y^{3})}^{2} \cdot (6 y)}$ .

$\sqrt{{(\frac{1}{y^{3}})}^{2} \frac{7 x}{6 y}}$

Step 2

Pull terms out from under the radical.

$\frac{1}{y^{3}} \sqrt{\frac{7 x}{6 y}}$

Step 3

Rewrite $\sqrt{\frac{7 x}{6 y}}$ as $\frac{\sqrt{7 x}}{\sqrt{6 y}}$ .

$\frac{1}{y^{3}} \cdot \frac{\sqrt{7 x}}{\sqrt{6 y}}$

Step 4

Combine.

$\frac{1 \sqrt{7 x}}{y^{3} \sqrt{6 y}}$

Step 5

Multiply $\sqrt{7 x}$ by $1$ .

$\frac{\sqrt{7 x}}{y^{3} \sqrt{6 y}}$

Step 6

Multiply $\frac{\sqrt{7 x}}{y^{3} \sqrt{6 y}}$ by $\frac{\sqrt{6 y}}{\sqrt{6 y}}$ .

$\frac{\sqrt{7 x}}{y^{3} \sqrt{6 y}} \cdot \frac{\sqrt{6 y}}{\sqrt{6 y}}$

Step 7

Combine and simplify the denominator.

Multiply $\frac{\sqrt{7 x}}{y^{3} \sqrt{6 y}}$ by $\frac{\sqrt{6 y}}{\sqrt{6 y}}$ .

$\frac{\sqrt{7 x} \sqrt{6 y}}{y^{3} \sqrt{6 y} \sqrt{6 y}}$

Move $\sqrt{6 y}$ .

$\frac{\sqrt{7 x} \sqrt{6 y}}{y^{3} (\sqrt{6 y} \sqrt{6 y})}$

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

$\frac{\sqrt{7 x} \sqrt{6 y}}{y^{3} ({\sqrt{6 y}}^{1} \sqrt{6 y})}$

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

$\frac{\sqrt{7 x} \sqrt{6 y}}{y^{3} ({\sqrt{6 y}}^{1} {\sqrt{6 y}}^{1})}$

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

$\frac{\sqrt{7 x} \sqrt{6 y}}{y^{3} {\sqrt{6 y}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{7 x} \sqrt{6 y}}{y^{3} {\sqrt{6 y}}^{2}}$

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

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

$\frac{\sqrt{7 x} \sqrt{6 y}}{y^{3} {({(6 y)}^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{7 x} \sqrt{6 y}}{y^{3} {(6 y)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{7 x} \sqrt{6 y}}{y^{3} {(6 y)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{7 x} \sqrt{6 y}}{y^{3} {(6 y)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{7 x} \sqrt{6 y}}{y^{3} {(6 y)}^{1}}$

Simplify.

$\frac{\sqrt{7 x} \sqrt{6 y}}{y^{3} (6 y)}$

Step 8

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

Move $y$ .

$\frac{\sqrt{7 x} \sqrt{6 y}}{y \cdot y^{3} \cdot 6}$

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

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

$\frac{\sqrt{7 x} \sqrt{6 y}}{y^{1} y^{3} \cdot 6}$

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

$\frac{\sqrt{7 x} \sqrt{6 y}}{y^{1 + 3} \cdot 6}$

Add $1$ and $3$ .

$\frac{\sqrt{7 x} \sqrt{6 y}}{y^{4} \cdot 6}$

Step 9

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{\sqrt{7 x (6 y)}}{y^{4} \cdot 6}$

Multiply $6$ by $7$ .

$\frac{\sqrt{42 x y}}{y^{4} \cdot 6}$

Step 10

Move $6$ to the left of $y^{4}$ .

$\frac{\sqrt{42 x y}}{6 y^{4}}$

Simplify square root of (7x)/(6y^7)

Related Questions

Support LCMGCF.com by disabling your adblocker.