Simplify square root of 250/48

$\sqrt{\frac{250}{48}}$

Cancel the common factor of $250$ and $48$ .

Factor $2$ out of $250$ .

$\sqrt{\frac{2 (125)}{48}}$

Cancel the common factors.

Factor $2$ out of $48$ .

$\sqrt{\frac{2 \cdot 125}{2 \cdot 24}}$

Cancel the common factor.

$\sqrt{\frac{2 \cdot 125}{2 \cdot 24}}$

Rewrite the expression.

$\sqrt{\frac{125}{24}}$

Rewrite $\sqrt{\frac{125}{24}}$ as $\frac{\sqrt{125}}{\sqrt{24}}$ .

$\frac{\sqrt{125}}{\sqrt{24}}$

Simplify the numerator.

Rewrite $125$ as $5^{2} \cdot 5$ .

Factor $25$ out of $125$ .

$\frac{\sqrt{25 (5)}}{\sqrt{24}}$

Rewrite $25$ as $5^{2}$ .

$\frac{\sqrt{5^{2} \cdot 5}}{\sqrt{24}}$

Pull terms out from under the radical.

$\frac{5 \sqrt{5}}{\sqrt{24}}$

Simplify the denominator.

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

$\frac{5 \sqrt{5}}{\sqrt{4 (6)}}$

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

$\frac{5 \sqrt{5}}{\sqrt{2^{2} \cdot 6}}$

Pull terms out from under the radical.

$\frac{5 \sqrt{5}}{2 \sqrt{6}}$

Multiply $\frac{5 \sqrt{5}}{2 \sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$\frac{5 \sqrt{5}}{2 \sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}}$

Combine and simplify the denominator.

Multiply $\frac{5 \sqrt{5}}{2 \sqrt{6}}$ by $\frac{\sqrt{6}}{\sqrt{6}}$ .

$\frac{5 \sqrt{5} \sqrt{6}}{2 \sqrt{6} \sqrt{6}}$

Move $\sqrt{6}$ .

$\frac{5 \sqrt{5} \sqrt{6}}{2 (\sqrt{6} \sqrt{6})}$

Raise $\sqrt{6}$ to the power of $1$ .

$\frac{5 \sqrt{5} \sqrt{6}}{2 ({\sqrt{6}}^{1} \sqrt{6})}$

Raise $\sqrt{6}$ to the power of $1$ .

$\frac{5 \sqrt{5} \sqrt{6}}{2 ({\sqrt{6}}^{1} {\sqrt{6}}^{1})}$

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

$\frac{5 \sqrt{5} \sqrt{6}}{2 {\sqrt{6}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{5 \sqrt{5} \sqrt{6}}{2 {\sqrt{6}}^{2}}$

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$\frac{5 \sqrt{5} \sqrt{6}}{2 {(6^{\frac{1}{2}})}^{2}}$

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

$\frac{5 \sqrt{5} \sqrt{6}}{2 \cdot 6^{\frac{1}{2} \cdot 2}}$

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

$\frac{5 \sqrt{5} \sqrt{6}}{2 \cdot 6^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5 \sqrt{5} \sqrt{6}}{2 \cdot 6^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{5 \sqrt{5} \sqrt{6}}{2 \cdot 6^{1}}$

Evaluate the exponent.

$\frac{5 \sqrt{5} \sqrt{6}}{2 \cdot 6}$

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{5 \sqrt{6 \cdot 5}}{2 \cdot 6}$

Multiply $6$ by $5$ .

$\frac{5 \sqrt{30}}{2 \cdot 6}$

Multiply $2$ by $6$ .

$\frac{5 \sqrt{30}}{12}$

The result can be shown in multiple forms.

Exact Form:

$\frac{5 \sqrt{30}}{12}$

Decimal Form:

$2.28217732 \dots$

Simplify square root of 250/48

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