Simplify 225/( square root of 15y)

$\frac{225}{\sqrt{15 y}}$

Step 1

Multiply $\frac{225}{\sqrt{15 y}}$ by $\frac{\sqrt{15 y}}{\sqrt{15 y}}$ .

$\frac{225}{\sqrt{15 y}} \cdot \frac{\sqrt{15 y}}{\sqrt{15 y}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{225}{\sqrt{15 y}}$ by $\frac{\sqrt{15 y}}{\sqrt{15 y}}$ .

$\frac{225 \sqrt{15 y}}{\sqrt{15 y} \sqrt{15 y}}$

Raise $\sqrt{15 y}$ to the power of $1$ .

$\frac{225 \sqrt{15 y}}{{\sqrt{15 y}}^{1} \sqrt{15 y}}$

Raise $\sqrt{15 y}$ to the power of $1$ .

$\frac{225 \sqrt{15 y}}{{\sqrt{15 y}}^{1} {\sqrt{15 y}}^{1}}$

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

$\frac{225 \sqrt{15 y}}{{\sqrt{15 y}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{225 \sqrt{15 y}}{{\sqrt{15 y}}^{2}}$

Rewrite ${\sqrt{15 y}}^{2}$ as $15 y$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{15 y}$ as ${(15 y)}^{\frac{1}{2}}$ .

$\frac{225 \sqrt{15 y}}{{({(15 y)}^{\frac{1}{2}})}^{2}}$

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

$\frac{225 \sqrt{15 y}}{{(15 y)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{225 \sqrt{15 y}}{{(15 y)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{225 \sqrt{15 y}}{{(15 y)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{225 \sqrt{15 y}}{{(15 y)}^{1}}$

Simplify.

$\frac{225 \sqrt{15 y}}{15 y}$

Step 3

Cancel the common factor of $225$ and $15$ .

Factor $15$ out of $225 \sqrt{15 y}$ .

$\frac{15 (15 \sqrt{15 y})}{15 y}$

Cancel the common factors.

Factor $15$ out of $15 y$ .

$\frac{15 (15 \sqrt{15 y})}{15 (y)}$

Cancel the common factor.

$\frac{15 (15 \sqrt{15 y})}{15 y}$

Rewrite the expression.

$\frac{15 \sqrt{15 y}}{y}$