Solve sqrt{15/10}=sqrt{(30/10)/2}

$$\sqrt { \frac { 15 } { 10 } } = \sqrt { \frac { ( \frac { 30 } { 10 } ) } { 2 } }$$

Verify

Solution Steps

Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{3}{2}}=\sqrt{\frac{\frac{30}{10}}{2}}$$

Rewrite the square root of the division \sqrt{\frac{3}{2}} as the division of square roots \frac{\sqrt{3}}{\sqrt{2}}.

$$\frac{\sqrt{3}}{\sqrt{2}}=\sqrt{\frac{\frac{30}{10}}{2}}$$

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}=\sqrt{\frac{\frac{30}{10}}{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{3}\sqrt{2}}{2}=\sqrt{\frac{\frac{30}{10}}{2}}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{2}=\sqrt{\frac{\frac{30}{10}}{2}}$$

Express \frac{\frac{30}{10}}{2} as a single fraction.

$$\frac{\sqrt{6}}{2}=\sqrt{\frac{30}{10\times 2}}$$

Multiply 10 and 2 to get 20.

$$\frac{\sqrt{6}}{2}=\sqrt{\frac{30}{20}}$$

Reduce the fraction \frac{30}{20} to lowest terms by extracting and canceling out 10.

$$\frac{\sqrt{6}}{2}=\sqrt{\frac{3}{2}}$$

Rewrite the square root of the division \sqrt{\frac{3}{2}} as the division of square roots \frac{\sqrt{3}}{\sqrt{2}}.

$$\frac{\sqrt{6}}{2}=\frac{\sqrt{3}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{6}}{2}=\frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{6}}{2}=\frac{\sqrt{3}\sqrt{2}}{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{2}=\frac{\sqrt{6}}{2}$$

Subtract \frac{\sqrt{6}}{2} from both sides.

$$\frac{\sqrt{6}}{2}-\frac{\sqrt{6}}{2}=0$$

Combine \frac{\sqrt{6}}{2} and -\frac{\sqrt{6}}{2} to get 0.

$$0=0$$

Compare 0 and 0.

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