Simplify square root of (x^5)/45

$\sqrt{\frac{x^{5}}{45}}$

Step 1

Rewrite $\frac{x^{5}}{45}$ as ${(\frac{x^{2}}{3})}^{2} \frac{x}{5}$ .

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

$\sqrt{\frac{{(x^{2})}^{2} x}{45}}$

Factor the perfect power $3^{2}$ out of $45$ .

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

Rearrange the fraction $\frac{{(x^{2})}^{2} x}{3^{2} \cdot 5}$ .

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

Step 2

Pull terms out from under the radical.

$\frac{x^{2}}{3} \sqrt{\frac{x}{5}}$

Step 3

Rewrite $\sqrt{\frac{x}{5}}$ as $\frac{\sqrt{x}}{\sqrt{5}}$ .

$\frac{x^{2}}{3} \cdot \frac{\sqrt{x}}{\sqrt{5}}$

Step 4

Combine.

$\frac{x^{2} \sqrt{x}}{3 \sqrt{5}}$

Step 5

Multiply $\frac{x^{2} \sqrt{x}}{3 \sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{x^{2} \sqrt{x}}{3 \sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

Step 6

Combine and simplify the denominator.

Multiply $\frac{x^{2} \sqrt{x}}{3 \sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{x^{2} \sqrt{x} \sqrt{5}}{3 \sqrt{5} \sqrt{5}}$

Move $\sqrt{5}$ .

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

Raise $\sqrt{5}$ to the power of $1$ .

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

Raise $\sqrt{5}$ to the power of $1$ .

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

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

$\frac{x^{2} \sqrt{x} \sqrt{5}}{3 {\sqrt{5}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{x^{2} \sqrt{x} \sqrt{5}}{3 {\sqrt{5}}^{2}}$

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

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

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

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

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

$\frac{x^{2} \sqrt{x} \sqrt{5}}{3 \cdot 5^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x^{2} \sqrt{x} \sqrt{5}}{3 \cdot 5^{\frac{2}{2}}}$

Rewrite the expression.

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

Evaluate the exponent.

$\frac{x^{2} \sqrt{x} \sqrt{5}}{3 \cdot 5}$

Step 7

Combine using the product rule for radicals.

$\frac{x^{2} \sqrt{5 x}}{3 \cdot 5}$

Step 8

Multiply $3$ by $5$ .

$\frac{x^{2} \sqrt{5 x}}{15}$

Simplify square root of (x^5)/45

Related Questions

Support LCMGCF.com by disabling your adblocker.