Solve sqrt{41/8}

$$\sqrt { 4 \frac { 1 } { 8 } }$$

Evaluate

$$\frac{\sqrt{66}}{4}\approx 2.031009601$$

Solution Steps

Multiply 4 and 8 to get 32.

$$\sqrt{\frac{32+1}{8}}$$

Add 32 and 1 to get 33.

$$\sqrt{\frac{33}{8}}$$

Rewrite the square root of the division \sqrt{\frac{33}{8}} as the division of square roots \frac{\sqrt{33}}{\sqrt{8}}.

$$\frac{\sqrt{33}}{\sqrt{8}}$$

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}.

$$\frac{\sqrt{33}}{2\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{33}}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{33}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{33}\sqrt{2}}{2\times 2}$$

To multiply \sqrt{33} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{66}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{66}}{4}$$