Solve sqrt{32^-3}

$$\sqrt { 32 ^ { - 3 } }$$

Evaluate

$$\frac{\sqrt{2}}{256}\approx 0.005524272$$

Solution Steps

Calculate 32 to the power of -3 and get \frac{1}{32768}.

$$\sqrt{\frac{1}{32768}}$$

Rewrite the square root of the division \sqrt{\frac{1}{32768}} as the division of square roots \frac{\sqrt{1}}{\sqrt{32768}}.

$$\frac{\sqrt{1}}{\sqrt{32768}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{32768}}$$

Factor 32768=128^{2}\times 2. Rewrite the square root of the product \sqrt{128^{2}\times 2} as the product of square roots \sqrt{128^{2}}\sqrt{2}. Take the square root of 128^{2}.

$$\frac{1}{128\sqrt{2}}$$

Rationalize the denominator of \frac{1}{128\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{2}}{128\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{128\times 2}$$

Multiply 128 and 2 to get 256.

$$\frac{\sqrt{2}}{256}$$