Solve frac{sqrt{8}}{sqrt{32}}*sqrt{8}

$$\frac{ \sqrt{ 8 } }{ \sqrt{ 32 } } \times \sqrt{ 8 }$$

Evaluate

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

Solution Steps

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}.

$$\frac{2\sqrt{2}}{\sqrt{32}}\sqrt{8}$$

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}.

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

Cancel out 2\sqrt{2} in both numerator and denominator.

$$\frac{1}{2}\sqrt{8}$$

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}.

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

Cancel out 2 and 2.

$$\sqrt{2}$$