Simplify 1/( square root of 40)

$\frac{1}{\sqrt{40}}$

Step 1

Simplify the denominator.

Rewrite

$40$ as

$2^{2} \cdot 10$ .

Factor

$4$ out of

$40$ .

$\frac{1}{\sqrt{4 (10)}}$

Rewrite

$4$ as

$2^{2}$ .

$\frac{1}{\sqrt{2^{2} \cdot 10}}$

Pull terms out from under the radical.

$\frac{1}{2 \sqrt{10}}$

Step 2

Multiply

$\frac{1}{2 \sqrt{10}}$ by

$\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{1}{2 \sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}$

Step 3

Combine and simplify the denominator.

Multiply

$\frac{1}{2 \sqrt{10}}$ by

$\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{\sqrt{10}}{2 \sqrt{10} \sqrt{10}}$

Move

$\sqrt{10}$ .

$\frac{\sqrt{10}}{2 (\sqrt{10} \sqrt{10})}$

Raise

$\sqrt{10}$ to the power of

$1$ .

$\frac{\sqrt{10}}{2 ({\sqrt{10}}^{1} \sqrt{10})}$

Raise

$\sqrt{10}$ to the power of

$1$ .

$\frac{\sqrt{10}}{2 ({\sqrt{10}}^{1} {\sqrt{10}}^{1})}$

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt{10}}{2 {\sqrt{10}}^{1 + 1}}$

Add

$1$ and

$1$ .

$\frac{\sqrt{10}}{2 {\sqrt{10}}^{2}}$

Rewrite

${\sqrt{10}}^{2}$ as

$10$ .

Use

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

$\sqrt{10}$ as

$10^{\frac{1}{2}}$ .

$\frac{\sqrt{10}}{2 {(10^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$\frac{\sqrt{10}}{2 \cdot 10^{\frac{1}{2} \cdot 2}}$

Combine

$\frac{1}{2}$ and

$2$ .

$\frac{\sqrt{10}}{2 \cdot 10^{\frac{2}{2}}}$

Cancel the common factor of

$2$ .

Cancel the common factor.

$\frac{\sqrt{10}}{2 \cdot 10^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{10}}{2 \cdot 10^{1}}$

Evaluate the exponent.

$\frac{\sqrt{10}}{2 \cdot 10}$

Step 4

Multiply

$2$ by

$10$ .

$\frac{\sqrt{10}}{20}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{10}}{20}$

Decimal Form:

$0.15811388 \dots$

Simplify 1/( square root of 40)

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