Solve 4sqrt{1/8}-sqrt{32}

$$4 \sqrt { \frac { 1 } { 8 } } - \sqrt { 32 }$$

Evaluate

$$-3\sqrt{2}\approx -4.242640687$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{8}} as the division of square roots \frac{\sqrt{1}}{\sqrt{8}}.

$$4\times \frac{\sqrt{1}}{\sqrt{8}}-\sqrt{32}$$

Calculate the square root of 1 and get 1.

$$4\times \frac{1}{\sqrt{8}}-\sqrt{32}$$

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}.

$$4\times \frac{1}{2\sqrt{2}}-\sqrt{32}$$

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

$$4\times \frac{\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}-\sqrt{32}$$

The square of \sqrt{2} is 2.

$$4\times \frac{\sqrt{2}}{2\times 2}-\sqrt{32}$$

Multiply 2 and 2 to get 4.

$$4\times \frac{\sqrt{2}}{4}-\sqrt{32}$$

Cancel out 4 and 4.

$$\sqrt{2}-\sqrt{32}$$

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}.

$$\sqrt{2}-4\sqrt{2}$$

Combine \sqrt{2} and -4\sqrt{2} to get -3\sqrt{2}.

$$-3\sqrt{2}$$