Solve 3sqrt{1/8}-3sqrt{1/8}

$$3 \sqrt { \frac { 1 } { 8 } } - 3 \sqrt { \frac { 1 } { 8 } }$$

Evaluate

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Short Solution Steps

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

$$3\times \frac{\sqrt{1}}{\sqrt{8}}-3\sqrt{\frac{1}{8}}$$

Calculate the square root of 1 and get 1.

$$3\times \frac{1}{\sqrt{8}}-3\sqrt{\frac{1}{8}}$$

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}.

$$3\times \frac{1}{2\sqrt{2}}-3\sqrt{\frac{1}{8}}$$

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

$$3\times \frac{\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}-3\sqrt{\frac{1}{8}}$$

The square of \sqrt{2} is 2.

$$3\times \frac{\sqrt{2}}{2\times 2}-3\sqrt{\frac{1}{8}}$$

Multiply 2 and 2 to get 4.

$$3\times \frac{\sqrt{2}}{4}-3\sqrt{\frac{1}{8}}$$

Express 3\times \frac{\sqrt{2}}{4} as a single fraction.

$$\frac{3\sqrt{2}}{4}-3\sqrt{\frac{1}{8}}$$

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

$$\frac{3\sqrt{2}}{4}-3\times \frac{\sqrt{1}}{\sqrt{8}}$$

Calculate the square root of 1 and get 1.

$$\frac{3\sqrt{2}}{4}-3\times \frac{1}{\sqrt{8}}$$

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}.

$$\frac{3\sqrt{2}}{4}-3\times \frac{1}{2\sqrt{2}}$$

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

$$\frac{3\sqrt{2}}{4}-3\times \frac{\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{2}}{4}-3\times \frac{\sqrt{2}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{3\sqrt{2}}{4}-3\times \frac{\sqrt{2}}{4}$$

Express -3\times \frac{\sqrt{2}}{4} as a single fraction.

$$\frac{3\sqrt{2}}{4}+\frac{-3\sqrt{2}}{4}$$

Since \frac{3\sqrt{2}}{4} and \frac{-3\sqrt{2}}{4} have the same denominator, add them by adding their numerators.

$$\frac{3\sqrt{2}-3\sqrt{2}}{4}$$

Do the calculations in 3\sqrt{2}-3\sqrt{2}.

$$\frac{0}{4}$$

Zero divided by any non-zero number gives zero.

$$0$$

Factor

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