Solve 8divsqrt{32}=

$$8 \div \sqrt{ 32 } =$$

Evaluate

$$\sqrt{2}\approx 1.414213562$$

Solution Steps

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}.

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

Rationalize the denominator of \frac{8}{4\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{8\sqrt{2}}{4\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

Cancel out 2\times 4 in both numerator and denominator.

$$\sqrt{2}$$