Simplify 15/(48 square root of 5/6)

$\frac{15}{48 \sqrt{\frac{5}{6}}}$

Step 1

Cancel the common factor of

$15$ and

$48$ .

Factor

$3$ out of

$15$ .

$\frac{3 (5)}{48 \sqrt{\frac{5}{6}}}$

Cancel the common factors.

Factor

$3$ out of

$48 \sqrt{\frac{5}{6}}$ .

$\frac{3 (5)}{3 (16 \sqrt{\frac{5}{6}})}$

Cancel the common factor.

$\frac{3 \cdot 5}{3 (16 \sqrt{\frac{5}{6}})}$

Rewrite the expression.

$\frac{5}{16 \sqrt{\frac{5}{6}}}$

Step 2

Simplify the denominator.

Rewrite

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

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

$\frac{5}{16 \frac{\sqrt{5}}{\sqrt{6}}}$

Multiply

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

$\frac{\sqrt{6}}{\sqrt{6}}$ .

$\frac{5}{16 (\frac{\sqrt{5}}{\sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}})}$

Combine and simplify the denominator.

Multiply

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

$\frac{\sqrt{6}}{\sqrt{6}}$ .

$\frac{5}{16 \frac{\sqrt{5} \sqrt{6}}{\sqrt{6} \sqrt{6}}}$

Raise

$\sqrt{6}$ to the power of

$1$ .

$\frac{5}{16 \frac{\sqrt{5} \sqrt{6}}{{\sqrt{6}}^{1} \sqrt{6}}}$

Raise

$\sqrt{6}$ to the power of

$1$ .

$\frac{5}{16 \frac{\sqrt{5} \sqrt{6}}{{\sqrt{6}}^{1} {\sqrt{6}}^{1}}}$

Use the power rule

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

$\frac{5}{16 \frac{\sqrt{5} \sqrt{6}}{{\sqrt{6}}^{1 + 1}}}$

Add

$1$ and

$1$ .

$\frac{5}{16 \frac{\sqrt{5} \sqrt{6}}{{\sqrt{6}}^{2}}}$

Rewrite

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

$6$ .

Use

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

$\sqrt{6}$ as

$6^{\frac{1}{2}}$ .

$\frac{5}{16 \frac{\sqrt{5} \sqrt{6}}{{(6^{\frac{1}{2}})}^{2}}}$

Apply the power rule and multiply exponents,

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

$\frac{5}{16 \frac{\sqrt{5} \sqrt{6}}{6^{\frac{1}{2} \cdot 2}}}$

Combine

$\frac{1}{2}$ and

$2$ .

$\frac{5}{16 \frac{\sqrt{5} \sqrt{6}}{6^{\frac{2}{2}}}}$

Cancel the common factor of

$2$ .

Cancel the common factor.

$\frac{5}{16 \frac{\sqrt{5} \sqrt{6}}{6^{\frac{2}{2}}}}$

Rewrite the expression.

$\frac{5}{16 \frac{\sqrt{5} \sqrt{6}}{6^{1}}}$

Evaluate the exponent.

$\frac{5}{16 \frac{\sqrt{5} \sqrt{6}}{6}}$

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{5}{16 \frac{\sqrt{5 \cdot 6}}{6}}$

Multiply

$5$ by

$6$ .

$\frac{5}{16 \frac{\sqrt{30}}{6}}$

Step 3

Simplify terms.

Combine

$16$ and

$\frac{\sqrt{30}}{6}$ .

$\frac{5}{\frac{16 \sqrt{30}}{6}}$

Reduce the expression

$\frac{16 \sqrt{30}}{6}$ by cancelling the common factors.

Factor

$2$ out of

$16 \sqrt{30}$ .

$\frac{5}{\frac{2 (8 \sqrt{30})}{6}}$

Factor

$2$ out of

$6$ .

$\frac{5}{\frac{2 (8 \sqrt{30})}{2 (3)}}$

Cancel the common factor.

$\frac{5}{\frac{2 (8 \sqrt{30})}{2 \cdot 3}}$

Rewrite the expression.

$\frac{5}{\frac{8 \sqrt{30}}{3}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$5 \frac{3}{8 \sqrt{30}}$

Step 5

Multiply

$\frac{3}{8 \sqrt{30}}$ by

$\frac{\sqrt{30}}{\sqrt{30}}$ .

$5 (\frac{3}{8 \sqrt{30}} \cdot \frac{\sqrt{30}}{\sqrt{30}})$

Step 6

Combine and simplify the denominator.

Multiply

$\frac{3}{8 \sqrt{30}}$ by

$\frac{\sqrt{30}}{\sqrt{30}}$ .

$5 \frac{3 \sqrt{30}}{8 \sqrt{30} \sqrt{30}}$

Move

$\sqrt{30}$ .

$5 \frac{3 \sqrt{30}}{8 (\sqrt{30} \sqrt{30})}$

Raise

$\sqrt{30}$ to the power of

$1$ .

$5 \frac{3 \sqrt{30}}{8 ({\sqrt{30}}^{1} \sqrt{30})}$

Raise

$\sqrt{30}$ to the power of

$1$ .

$5 \frac{3 \sqrt{30}}{8 ({\sqrt{30}}^{1} {\sqrt{30}}^{1})}$

Use the power rule

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

$5 \frac{3 \sqrt{30}}{8 {\sqrt{30}}^{1 + 1}}$

Add

$1$ and

$1$ .

$5 \frac{3 \sqrt{30}}{8 {\sqrt{30}}^{2}}$

Rewrite

${\sqrt{30}}^{2}$ as

$30$ .

Use

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

$\sqrt{30}$ as

$30^{\frac{1}{2}}$ .

$5 \frac{3 \sqrt{30}}{8 {(30^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents,

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

$5 \frac{3 \sqrt{30}}{8 \cdot 30^{\frac{1}{2} \cdot 2}}$

Combine

$\frac{1}{2}$ and

$2$ .

$5 \frac{3 \sqrt{30}}{8 \cdot 30^{\frac{2}{2}}}$

Cancel the common factor of

$2$ .

Cancel the common factor.

$5 \frac{3 \sqrt{30}}{8 \cdot 30^{\frac{2}{2}}}$

Rewrite the expression.

$5 \frac{3 \sqrt{30}}{8 \cdot 30^{1}}$

Evaluate the exponent.

$5 \frac{3 \sqrt{30}}{8 \cdot 30}$

Step 7

Cancel the common factor of

$3$ and

$30$ .

Factor

$3$ out of

$3 \sqrt{30}$ .

$5 \frac{3 (\sqrt{30})}{8 \cdot 30}$

Cancel the common factors.

Factor

$3$ out of

$8 \cdot 30$ .

$5 \frac{3 (\sqrt{30})}{3 (8 \cdot 10)}$

Cancel the common factor.

$5 \frac{3 \sqrt{30}}{3 (8 \cdot 10)}$

Rewrite the expression.

$5 \frac{\sqrt{30}}{8 \cdot 10}$

Step 8

Multiply

$8$ by

$10$ .

$5 \frac{\sqrt{30}}{80}$

Step 9

Cancel the common factor of

$5$ .

Factor

$5$ out of

$80$ .

$5 \frac{\sqrt{30}}{5 (16)}$

Cancel the common factor.

$5 \frac{\sqrt{30}}{5 \cdot 16}$

Rewrite the expression.

$\frac{\sqrt{30}}{16}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{30}}{16}$

Decimal Form:

$0.34232659 \dots$

Simplify 15/(48 square root of 5/6)

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