Solve 6sqrt{1/8}-sqrt{32}

$$6 \sqrt{ \frac{ 1 }{ 8 } } - \sqrt{ 32 }$$

Evaluate

$$-\frac{5\sqrt{2}}{2}\approx -3.535533906$$

Solution Steps

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

$$6\times \frac{\sqrt{1}}{\sqrt{8}}-\sqrt{32}$$

Calculate the square root of 1 and get 1.

$$6\times \frac{1}{\sqrt{8}}-\sqrt{32}$$

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}.

$$6\times \frac{1}{2\sqrt{2}}-\sqrt{32}$$

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

$$6\times \frac{\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}-\sqrt{32}$$

The square of \sqrt{2} is 2.

$$6\times \frac{\sqrt{2}}{2\times 2}-\sqrt{32}$$

Multiply 2 and 2 to get 4.

$$6\times \frac{\sqrt{2}}{4}-\sqrt{32}$$

Express 6\times \frac{\sqrt{2}}{4} as a single fraction.

$$\frac{6\sqrt{2}}{4}-\sqrt{32}$$

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}.

$$\frac{6\sqrt{2}}{4}-4\sqrt{2}$$

Combine \frac{6\sqrt{2}}{4} and -4\sqrt{2} to get -\frac{5}{2}\sqrt{2}.

$$-\frac{5}{2}\sqrt{2}$$