Simplify square root of 3/(y^5)

$\sqrt{\frac{3}{y^{5}}}$

Step 1

Rewrite $\frac{3}{y^{5}}$ as ${(\frac{1}{y^{2}})}^{2} \frac{3}{y}$ .

Factor the perfect power $1^{2}$ out of $3$ .

$\sqrt{\frac{1^{2} \cdot 3}{y^{5}}}$

Factor the perfect power ${(y^{2})}^{2}$ out of $y^{5}$ .

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

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

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

Step 2

Pull terms out from under the radical.

$\frac{1}{y^{2}} \sqrt{\frac{3}{y}}$

Step 3

Rewrite $\sqrt{\frac{3}{y}}$ as $\frac{\sqrt{3}}{\sqrt{y}}$ .

$\frac{1}{y^{2}} \cdot \frac{\sqrt{3}}{\sqrt{y}}$

Step 4

Combine.

$\frac{1 \sqrt{3}}{y^{2} \sqrt{y}}$

Step 5

Multiply $\sqrt{3}$ by $1$ .

$\frac{\sqrt{3}}{y^{2} \sqrt{y}}$

Step 6

Multiply $\frac{\sqrt{3}}{y^{2} \sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

$\frac{\sqrt{3}}{y^{2} \sqrt{y}} \cdot \frac{\sqrt{y}}{\sqrt{y}}$

Step 7

Combine and simplify the denominator.

Multiply $\frac{\sqrt{3}}{y^{2} \sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

$\frac{\sqrt{3} \sqrt{y}}{y^{2} \sqrt{y} \sqrt{y}}$

Move $\sqrt{y}$ .

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

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

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

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

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

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

$\frac{\sqrt{3} \sqrt{y}}{y^{2} {\sqrt{y}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{3} \sqrt{y}}{y^{2} {\sqrt{y}}^{2}}$

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

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

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

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

$\frac{\sqrt{3} \sqrt{y}}{y^{2} y^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{3} \sqrt{y}}{y^{2} y^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{3} \sqrt{y}}{y^{2} y^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{3} \sqrt{y}}{y^{2} y^{1}}$

Simplify.

$\frac{\sqrt{3} \sqrt{y}}{y^{2} y}$

Step 8

Multiply $y^{2}$ by $y$ by adding the exponents.

Multiply $y^{2}$ by $y$ .

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

$\frac{\sqrt{3} \sqrt{y}}{y^{2} y^{1}}$

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

$\frac{\sqrt{3} \sqrt{y}}{y^{2 + 1}}$

Add $2$ and $1$ .

$\frac{\sqrt{3} \sqrt{y}}{y^{3}}$

Step 9

Combine using the product rule for radicals.

$\frac{\sqrt{3 y}}{y^{3}}$

Simplify square root of 3/(y^5)

Related Questions

Support LCMGCF.com by disabling your adblocker.