Solve sqrt{9/8}

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

Evaluate

$$\frac{3\sqrt{2}}{4}\approx 1.060660172$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{9}{8}} as the division of square roots \frac{\sqrt{9}}{\sqrt{8}}.

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

Calculate the square root of 9 and get 3.

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

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}.

$$\frac{3}{2\sqrt{2}}$$

Rationalize the denominator of \frac{3}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{2}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{3\sqrt{2}}{4}$$