Simplify square root of 3/10

$\sqrt{\frac{3}{10}}$

Step 1

Rewrite $\sqrt{\frac{3}{10}}$ as $\frac{\sqrt{3}}{\sqrt{10}}$ .

$\frac{\sqrt{3}}{\sqrt{10}}$

Step 2

Multiply $\frac{\sqrt{3}}{\sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{\sqrt{3}}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{\sqrt{3}}{\sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{\sqrt{3} \sqrt{10}}{\sqrt{10} \sqrt{10}}$

Raise $\sqrt{10}$ to the power of $1$ .

$\frac{\sqrt{3} \sqrt{10}}{{\sqrt{10}}^{1} \sqrt{10}}$

Raise $\sqrt{10}$ to the power of $1$ .

$\frac{\sqrt{3} \sqrt{10}}{{\sqrt{10}}^{1} {\sqrt{10}}^{1}}$

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

$\frac{\sqrt{3} \sqrt{10}}{{\sqrt{10}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{3} \sqrt{10}}{{\sqrt{10}}^{2}}$

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

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$\frac{\sqrt{3} \sqrt{10}}{{(10^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{3} \sqrt{10}}{10^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{3} \sqrt{10}}{10^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{3} \sqrt{10}}{10^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{3} \sqrt{10}}{10^{1}}$

Evaluate the exponent.

$\frac{\sqrt{3} \sqrt{10}}{10}$

Step 4

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{\sqrt{3 \cdot 10}}{10}$

Multiply $3$ by $10$ .

$\frac{\sqrt{30}}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{30}}{10}$

Decimal Form:

$0.54772255 \dots$