Simplify 1/( square root of 17)

$\frac{1}{\sqrt{17}}$

Step 1

Multiply $\frac{1}{\sqrt{17}}$ by $\frac{\sqrt{17}}{\sqrt{17}}$ .

$\frac{1}{\sqrt{17}} \cdot \frac{\sqrt{17}}{\sqrt{17}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{17}}$ by $\frac{\sqrt{17}}{\sqrt{17}}$ .

$\frac{\sqrt{17}}{\sqrt{17} \sqrt{17}}$

Raise $\sqrt{17}$ to the power of $1$ .

$\frac{\sqrt{17}}{{\sqrt{17}}^{1} \sqrt{17}}$

Raise $\sqrt{17}$ to the power of $1$ .

$\frac{\sqrt{17}}{{\sqrt{17}}^{1} {\sqrt{17}}^{1}}$

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

$\frac{\sqrt{17}}{{\sqrt{17}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{17}}{{\sqrt{17}}^{2}}$

Rewrite ${\sqrt{17}}^{2}$ as $17$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{17}$ as $17^{\frac{1}{2}}$ .

$\frac{\sqrt{17}}{{(17^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{17}}{17^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{17}}{17^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{17}}{17^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{17}}{17^{1}}$

Evaluate the exponent.

$\frac{\sqrt{17}}{17}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{17}}{17}$

Decimal Form:

$0.24253562 \dots$