Solve sqrt{15/6^2-7*2+31}

$$\sqrt{ \frac{ 15 }{ { 6 }^{ 2 } -7 \cdot 2 } +31 }$$

Evaluate

$$\frac{\sqrt{15334}}{22}\approx 5.628660425$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$\sqrt{\frac{15}{36-7\times 2}+31}$$

Multiply 7 and 2 to get 14.

$$\sqrt{\frac{15}{36-14}+31}$$

Subtract 14 from 36 to get 22.

$$\sqrt{\frac{15}{22}+31}$$

Convert 31 to fraction \frac{682}{22}.

$$\sqrt{\frac{15}{22}+\frac{682}{22}}$$

Since \frac{15}{22} and \frac{682}{22} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{15+682}{22}}$$

Add 15 and 682 to get 697.

$$\sqrt{\frac{697}{22}}$$

Rewrite the square root of the division \sqrt{\frac{697}{22}} as the division of square roots \frac{\sqrt{697}}{\sqrt{22}}.

$$\frac{\sqrt{697}}{\sqrt{22}}$$

Rationalize the denominator of \frac{\sqrt{697}}{\sqrt{22}} by multiplying numerator and denominator by \sqrt{22}.

$$\frac{\sqrt{697}\sqrt{22}}{\left(\sqrt{22}\right)^{2}}$$

The square of \sqrt{22} is 22.

$$\frac{\sqrt{697}\sqrt{22}}{22}$$

To multiply \sqrt{697} and \sqrt{22}, multiply the numbers under the square root.

$$\frac{\sqrt{15334}}{22}$$