Solve sqrt{78*45/12}

$$\sqrt{ 78 \times \frac{ 45 }{ 12 } }$$

Evaluate

$$\frac{3\sqrt{130}}{2}\approx 17.102631376$$

Solution Steps

Reduce the fraction \frac{45}{12} to lowest terms by extracting and canceling out 3.

$$\sqrt{78\times \frac{15}{4}}$$

Express 78\times \frac{15}{4} as a single fraction.

$$\sqrt{\frac{78\times 15}{4}}$$

Multiply 78 and 15 to get 1170.

$$\sqrt{\frac{1170}{4}}$$

Reduce the fraction \frac{1170}{4} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{585}{2}}$$

Rewrite the square root of the division \sqrt{\frac{585}{2}} as the division of square roots \frac{\sqrt{585}}{\sqrt{2}}.

$$\frac{\sqrt{585}}{\sqrt{2}}$$

Factor 585=3^{2}\times 65. Rewrite the square root of the product \sqrt{3^{2}\times 65} as the product of square roots \sqrt{3^{2}}\sqrt{65}. Take the square root of 3^{2}.

$$\frac{3\sqrt{65}}{\sqrt{2}}$$

Rationalize the denominator of \frac{3\sqrt{65}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{3\sqrt{65}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{65}\sqrt{2}}{2}$$

To multiply \sqrt{65} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{3\sqrt{130}}{2}$$