Solve sqrt{78/56*2+6}

$$\sqrt{ \frac{ 78 }{ 56 \times 2+6 } }$$

Evaluate

$$\frac{\sqrt{2301}}{59}\approx 0.813029488$$

Solution Steps

Multiply 56 and 2 to get 112.

$$\sqrt{\frac{78}{112+6}}$$

Add 112 and 6 to get 118.

$$\sqrt{\frac{78}{118}}$$

Reduce the fraction \frac{78}{118} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{39}{59}}$$

Rewrite the square root of the division \sqrt{\frac{39}{59}} as the division of square roots \frac{\sqrt{39}}{\sqrt{59}}.

$$\frac{\sqrt{39}}{\sqrt{59}}$$

Rationalize the denominator of \frac{\sqrt{39}}{\sqrt{59}} by multiplying numerator and denominator by \sqrt{59}.

$$\frac{\sqrt{39}\sqrt{59}}{\left(\sqrt{59}\right)^{2}}$$

The square of \sqrt{59} is 59.

$$\frac{\sqrt{39}\sqrt{59}}{59}$$

To multiply \sqrt{39} and \sqrt{59}, multiply the numbers under the square root.

$$\frac{\sqrt{2301}}{59}$$