Solve sqrt{64/279}

$$\sqrt{ \frac{ 64 }{ 279 } }$$

Evaluate

$$\frac{8\sqrt{31}}{93}\approx 0.478947472$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{64}{279}} as the division of square roots \frac{\sqrt{64}}{\sqrt{279}}.

$$\frac{\sqrt{64}}{\sqrt{279}}$$

Calculate the square root of 64 and get 8.

$$\frac{8}{\sqrt{279}}$$

Factor 279=3^{2}\times 31. Rewrite the square root of the product \sqrt{3^{2}\times 31} as the product of square roots \sqrt{3^{2}}\sqrt{31}. Take the square root of 3^{2}.

$$\frac{8}{3\sqrt{31}}$$

Rationalize the denominator of \frac{8}{3\sqrt{31}} by multiplying numerator and denominator by \sqrt{31}.

$$\frac{8\sqrt{31}}{3\left(\sqrt{31}\right)^{2}}$$

The square of \sqrt{31} is 31.

$$\frac{8\sqrt{31}}{3\times 31}$$

Multiply 3 and 31 to get 93.

$$\frac{8\sqrt{31}}{93}$$