Simplify 1/( square root of 15)

$\frac{1}{\sqrt{15}}$

Step 1

Multiply $\frac{1}{\sqrt{15}}$ by $\frac{\sqrt{15}}{\sqrt{15}}$ .

$\frac{1}{\sqrt{15}} \cdot \frac{\sqrt{15}}{\sqrt{15}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{15}}$ by $\frac{\sqrt{15}}{\sqrt{15}}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

$\frac{\sqrt{15}}{15^{\frac{1}{2} \cdot 2}}$

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.25819888 \dots$