Solve sqrt{3div4*10}

$$\sqrt{ 3 \div 4 \times 10 }$$

Evaluate

$$\frac{\sqrt{30}}{2}\approx 2.738612788$$

Solution Steps

Express \frac{3}{4}\times 10 as a single fraction.

$$\sqrt{\frac{3\times 10}{4}}$$

Multiply 3 and 10 to get 30.

$$\sqrt{\frac{30}{4}}$$

Reduce the fraction \frac{30}{4} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{15}{2}}$$

Rewrite the square root of the division \sqrt{\frac{15}{2}} as the division of square roots \frac{\sqrt{15}}{\sqrt{2}}.

$$\frac{\sqrt{15}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{15}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{15}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{15}\sqrt{2}}{2}$$

To multiply \sqrt{15} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{30}}{2}$$