Solve 4sqrt{1/32}

$$4 \sqrt { \frac { 1 } { 32 } }$$

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{32}} as the division of square roots \frac{\sqrt{1}}{\sqrt{32}}.

$$4\times \frac{\sqrt{1}}{\sqrt{32}}$$

Calculate the square root of 1 and get 1.

$$4\times \frac{1}{\sqrt{32}}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$4\times \frac{1}{4\sqrt{2}}$$

Rationalize the denominator of \frac{1}{4\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$4\times \frac{\sqrt{2}}{4\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

Multiply 4 and 2 to get 8.

$$4\times \frac{\sqrt{2}}{8}$$

Cancel out 8, the greatest common factor in 4 and 8.

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