Solve 1/sqrt{frac{8{9}}}

$$\frac{ 1 }{ \sqrt{ \frac{ 8 }{ 9 } } }$$

Evaluate

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

Solution Steps

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

$$\frac{1}{\frac{\sqrt{8}}{\sqrt{9}}}$$

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}.

$$\frac{1}{\frac{2\sqrt{2}}{\sqrt{9}}}$$

Calculate the square root of 9 and get 3.

$$\frac{1}{\frac{2\sqrt{2}}{3}}$$

Divide 1 by \frac{2\sqrt{2}}{3} by multiplying 1 by the reciprocal of \frac{2\sqrt{2}}{3}.

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

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.

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