Solve 3sqrt{1/512}

$$3 \sqrt{ \frac{ 1 }{ 512 } }$$

Evaluate

$$\frac{3\sqrt{2}}{32}\approx 0.132582521$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{512}} as the division of square roots \frac{\sqrt{1}}{\sqrt{512}}.

$$3\times \frac{\sqrt{1}}{\sqrt{512}}$$

Calculate the square root of 1 and get 1.

$$3\times \frac{1}{\sqrt{512}}$$

Factor 512=16^{2}\times 2. Rewrite the square root of the product \sqrt{16^{2}\times 2} as the product of square roots \sqrt{16^{2}}\sqrt{2}. Take the square root of 16^{2}.

$$3\times \frac{1}{16\sqrt{2}}$$

Rationalize the denominator of \frac{1}{16\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$3\times \frac{\sqrt{2}}{16\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$3\times \frac{\sqrt{2}}{16\times 2}$$

Multiply 16 and 2 to get 32.

$$3\times \frac{\sqrt{2}}{32}$$

Express 3\times \frac{\sqrt{2}}{32} as a single fraction.

$$\frac{3\sqrt{2}}{32}$$