Solve 5sqrt{5/82xfrac{52{5(6x)}}}

$$5 \sqrt{ \frac{ 5 }{ 82x \frac{ 52 }{ 5(6x) } } }$$

Evaluate

$$\frac{25\sqrt{1599}}{1066}\approx 0.937793106$$

Solution Steps

Multiply 5 and 6 to get 30.

$$5\sqrt{\frac{5}{82x\times \frac{52}{30x}}}$$

Express 82\times \frac{52}{30x} as a single fraction.

$$5\sqrt{\frac{5}{\frac{82\times 52}{30x}x}}$$

Cancel out 2 in both numerator and denominator.

$$5\sqrt{\frac{5}{\frac{41\times 52}{15x}x}}$$

Multiply 41 and 52 to get 2132.

$$5\sqrt{\frac{5}{\frac{2132}{15x}x}}$$

Express \frac{2132}{15x}x as a single fraction.

$$5\sqrt{\frac{5}{\frac{2132x}{15x}}}$$

Cancel out x in both numerator and denominator.

$$5\sqrt{\frac{5}{\frac{2132}{15}}}$$

Divide 5 by \frac{2132}{15} by multiplying 5 by the reciprocal of \frac{2132}{15}.

$$5\sqrt{5\times \frac{15}{2132}}$$

Express 5\times \frac{15}{2132} as a single fraction.

$$5\sqrt{\frac{5\times 15}{2132}}$$

Multiply 5 and 15 to get 75.

$$5\sqrt{\frac{75}{2132}}$$

Rewrite the square root of the division \sqrt{\frac{75}{2132}} as the division of square roots \frac{\sqrt{75}}{\sqrt{2132}}.

$$5\times \frac{\sqrt{75}}{\sqrt{2132}}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$5\times \frac{5\sqrt{3}}{\sqrt{2132}}$$

Factor 2132=2^{2}\times 533. Rewrite the square root of the product \sqrt{2^{2}\times 533} as the product of square roots \sqrt{2^{2}}\sqrt{533}. Take the square root of 2^{2}.

$$5\times \frac{5\sqrt{3}}{2\sqrt{533}}$$

Rationalize the denominator of \frac{5\sqrt{3}}{2\sqrt{533}} by multiplying numerator and denominator by \sqrt{533}.

$$5\times \frac{5\sqrt{3}\sqrt{533}}{2\left(\sqrt{533}\right)^{2}}$$

The square of \sqrt{533} is 533.

$$5\times \frac{5\sqrt{3}\sqrt{533}}{2\times 533}$$

To multiply \sqrt{3} and \sqrt{533}, multiply the numbers under the square root.

$$5\times \frac{5\sqrt{1599}}{2\times 533}$$

Multiply 2 and 533 to get 1066.

$$5\times \frac{5\sqrt{1599}}{1066}$$

Express 5\times \frac{5\sqrt{1599}}{1066} as a single fraction.

$$\frac{5\times 5\sqrt{1599}}{1066}$$

Multiply 5 and 5 to get 25.

$$\frac{25\sqrt{1599}}{1066}$$