Simplify 5/( square root of 8)

$\frac{5}{\sqrt{8}}$

Step 1

Simplify the denominator.

Rewrite

$8$ as

$2^{2} \cdot 2$ .

Factor

$4$ out of

$8$ .

$\frac{5}{\sqrt{4 (2)}}$

Rewrite

$4$ as

$2^{2}$ .

$\frac{5}{\sqrt{2^{2} \cdot 2}}$

Pull terms out from under the radical.

$\frac{5}{2 \sqrt{2}}$

Step 2

Multiply

$\frac{5}{2 \sqrt{2}}$ by

$\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{5}{2 \sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$

Step 3

Combine and simplify the denominator.

Multiply

$\frac{5}{2 \sqrt{2}}$ by

$\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{5 \sqrt{2}}{2 \sqrt{2} \sqrt{2}}$

Move

$\sqrt{2}$ .

$\frac{5 \sqrt{2}}{2 (\sqrt{2} \sqrt{2})}$

Raise

$\sqrt{2}$ to the power of

$1$ .

$\frac{5 \sqrt{2}}{2 ({\sqrt{2}}^{1} \sqrt{2})}$

Raise

$\sqrt{2}$ to the power of

$1$ .

$\frac{5 \sqrt{2}}{2 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})}$

Use the power rule

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

$\frac{5 \sqrt{2}}{2 {\sqrt{2}}^{1 + 1}}$

Add

$1$ and

$1$ .

$\frac{5 \sqrt{2}}{2 {\sqrt{2}}^{2}}$

Rewrite

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

$2$ .

Use

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

$\sqrt{2}$ as

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

$\frac{5 \sqrt{2}}{2 {(2^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents,

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

$\frac{5 \sqrt{2}}{2 \cdot 2^{\frac{1}{2} \cdot 2}}$

Combine

$\frac{1}{2}$ and

$2$ .

$\frac{5 \sqrt{2}}{2 \cdot 2^{\frac{2}{2}}}$

Cancel the common factor of

$2$ .

Cancel the common factor.

$\frac{5 \sqrt{2}}{2 \cdot 2^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{5 \sqrt{2}}{2 \cdot 2^{1}}$

Evaluate the exponent.

$\frac{5 \sqrt{2}}{2 \cdot 2}$

Step 4

Multiply

$2$ by

$2$ .

$\frac{5 \sqrt{2}}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5 \sqrt{2}}{4}$

Decimal Form:

$1.76776695 \dots$

Simplify 5/( square root of 8)

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