Evaluate 4/( square root of 21)

$\frac{4}{\sqrt{21}}$

Step 1

Multiply $\frac{4}{\sqrt{21}}$ by $\frac{\sqrt{21}}{\sqrt{21}}$ .

$\frac{4}{\sqrt{21}} \cdot \frac{\sqrt{21}}{\sqrt{21}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{4}{\sqrt{21}}$ by $\frac{\sqrt{21}}{\sqrt{21}}$ .

$\frac{4 \sqrt{21}}{\sqrt{21} \sqrt{21}}$

Raise $\sqrt{21}$ to the power of $1$ .

$\frac{4 \sqrt{21}}{{\sqrt{21}}^{1} \sqrt{21}}$

Raise $\sqrt{21}$ to the power of $1$ .

$\frac{4 \sqrt{21}}{{\sqrt{21}}^{1} {\sqrt{21}}^{1}}$

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

$\frac{4 \sqrt{21}}{{\sqrt{21}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{4 \sqrt{21}}{{\sqrt{21}}^{2}}$

Rewrite ${\sqrt{21}}^{2}$ as $21$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{21}$ as $21^{\frac{1}{2}}$ .

$\frac{4 \sqrt{21}}{{(21^{\frac{1}{2}})}^{2}}$

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

$\frac{4 \sqrt{21}}{21^{\frac{1}{2} \cdot 2}}$

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

$\frac{4 \sqrt{21}}{21^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4 \sqrt{21}}{21^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{4 \sqrt{21}}{21^{1}}$

Evaluate the exponent.

$\frac{4 \sqrt{21}}{21}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{4 \sqrt{21}}{21}$

Decimal Form:

$0.87287156 \dots$