Solve sqrt{(1+6^2)[(144/36)^2-4*121/36}

$$\sqrt { ( 1 + 6 ^ { 2 } ) [ ( \frac { 144 } { 36 } ) ^ { 2 } - 4 \times \frac { 121 } { 36 } }$$

Evaluate

$$\frac{\sqrt{851}}{3}\approx 9.723968097$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$\sqrt{\left(1+36\right)\left(\left(\frac{144}{36}\right)^{2}-4\times \frac{121}{36}\right)}$$

Add 1 and 36 to get 37.

$$\sqrt{37\left(\left(\frac{144}{36}\right)^{2}-4\times \frac{121}{36}\right)}$$

Divide 144 by 36 to get 4.

$$\sqrt{37\left(4^{2}-4\times \frac{121}{36}\right)}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{37\left(16-4\times \frac{121}{36}\right)}$$

Multiply 4 and \frac{121}{36} to get \frac{121}{9}.

$$\sqrt{37\left(16-\frac{121}{9}\right)}$$

Subtract \frac{121}{9} from 16 to get \frac{23}{9}.

$$\sqrt{37\times \frac{23}{9}}$$

Multiply 37 and \frac{23}{9} to get \frac{851}{9}.

$$\sqrt{\frac{851}{9}}$$

Rewrite the square root of the division \sqrt{\frac{851}{9}} as the division of square roots \frac{\sqrt{851}}{\sqrt{9}}.

$$\frac{\sqrt{851}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{\sqrt{851}}{3}$$