Solve frac{5sqrt{8}}{4sqrt{52}}

$$\frac{ 5 \sqrt{ 8 } }{ 4 \sqrt{ 52 } }$$

Evaluate

$$\frac{5\sqrt{26}}{52}\approx 0.490290338$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{5\times 2\sqrt{2}}{4\sqrt{52}}$$

Multiply 5 and 2 to get 10.

$$\frac{10\sqrt{2}}{4\sqrt{52}}$$

Factor 52=2^{2}\times 13. Rewrite the square root of the product \sqrt{2^{2}\times 13} as the product of square roots \sqrt{2^{2}}\sqrt{13}. Take the square root of 2^{2}.

$$\frac{10\sqrt{2}}{4\times 2\sqrt{13}}$$

Multiply 4 and 2 to get 8.

$$\frac{10\sqrt{2}}{8\sqrt{13}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5\sqrt{2}}{4\sqrt{13}}$$

Rationalize the denominator of \frac{5\sqrt{2}}{4\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{5\sqrt{2}\sqrt{13}}{4\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{5\sqrt{2}\sqrt{13}}{4\times 13}$$

To multiply \sqrt{2} and \sqrt{13}, multiply the numbers under the square root.

$$\frac{5\sqrt{26}}{4\times 13}$$

Multiply 4 and 13 to get 52.

$$\frac{5\sqrt{26}}{52}$$