Solve sqrt{81/8}

$$\sqrt { \frac { 81 } { 8 } }$$

Evaluate

$$\frac{9\sqrt{2}}{4}\approx 3.181980515$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{81}{8}} as the division of square roots \frac{\sqrt{81}}{\sqrt{8}}.

$$\frac{\sqrt{81}}{\sqrt{8}}$$

Calculate the square root of 81 and get 9.

$$\frac{9}{\sqrt{8}}$$

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}.

$$\frac{9}{2\sqrt{2}}$$

Rationalize the denominator of \frac{9}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{9\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{9\sqrt{2}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{9\sqrt{2}}{4}$$