Simplify - square root of 4/7

$- \sqrt{\frac{4}{7}}$

Step 1

Rewrite $\sqrt{\frac{4}{7}}$ as $\frac{\sqrt{4}}{\sqrt{7}}$ .

$- \frac{\sqrt{4}}{\sqrt{7}}$

Step 2

Simplify the numerator.

Rewrite $4$ as $2^{2}$ .

$- \frac{\sqrt{2^{2}}}{\sqrt{7}}$

Pull terms out from under the radical, assuming positive real numbers.

$- \frac{2}{\sqrt{7}}$

Step 3

Multiply $\frac{2}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$- (\frac{2}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}})$

Step 4

Combine and simplify the denominator.

Multiply $\frac{2}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$- \frac{2 \sqrt{7}}{\sqrt{7} \sqrt{7}}$

Raise $\sqrt{7}$ to the power of $1$ .

$- \frac{2 \sqrt{7}}{{\sqrt{7}}^{1} \sqrt{7}}$

Raise $\sqrt{7}$ to the power of $1$ .

$- \frac{2 \sqrt{7}}{{\sqrt{7}}^{1} {\sqrt{7}}^{1}}$

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

$- \frac{2 \sqrt{7}}{{\sqrt{7}}^{1 + 1}}$

Add $1$ and $1$ .

$- \frac{2 \sqrt{7}}{{\sqrt{7}}^{2}}$

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$- \frac{2 \sqrt{7}}{{(7^{\frac{1}{2}})}^{2}}$

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

$- \frac{2 \sqrt{7}}{7^{\frac{1}{2} \cdot 2}}$

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

$- \frac{2 \sqrt{7}}{7^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{2 \sqrt{7}}{7^{\frac{2}{2}}}$

Rewrite the expression.

$- \frac{2 \sqrt{7}}{7^{1}}$

Evaluate the exponent.

$- \frac{2 \sqrt{7}}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{2 \sqrt{7}}{7}$

Decimal Form:

$- 0.75592894 \dots$