Find the Reciprocal square root of 40

$\sqrt{40}$

To find the reciprocal, divide $1$ by the number given.

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

Simplify.

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.

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

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

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

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.

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

Multiply $2$ by $10$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.15811388 \dots$

Find the Reciprocal square root of 40

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