Solve sqrt{25/8}

$$\sqrt{ \frac{ 25 }{ 8 } }$$

Evaluate

$$\frac{5\sqrt{2}}{4}\approx 1.767766953$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{25}{8}} as the division of square roots \frac{\sqrt{25}}{\sqrt{8}}.

$$\frac{\sqrt{25}}{\sqrt{8}}$$

Calculate the square root of 25 and get 5.

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

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}.

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

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

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

The square of \sqrt{2} is 2.

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

Multiply 2 and 2 to get 4.

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