Solve sqrt{(frac{6sqrt{31}}{2})^2+(6/2)^2}

$$\sqrt { ( \frac { 6 \sqrt { 31 } } { 2 } ) ^ { 2 } + ( \frac { 6 } { 2 } ) ^ { 2 } }$$

Evaluate

$$12\sqrt{2}\approx 16.970562748$$

Solution Steps

Divide 6\sqrt{31} by 2 to get 3\sqrt{31}.

$$\sqrt{\left(3\sqrt{31}\right)^{2}+\left(\frac{6}{2}\right)^{2}}$$

Expand \left(3\sqrt{31}\right)^{2}.

$$\sqrt{3^{2}\left(\sqrt{31}\right)^{2}+\left(\frac{6}{2}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{9\left(\sqrt{31}\right)^{2}+\left(\frac{6}{2}\right)^{2}}$$

The square of \sqrt{31} is 31.

$$\sqrt{9\times 31+\left(\frac{6}{2}\right)^{2}}$$

Multiply 9 and 31 to get 279.

$$\sqrt{279+\left(\frac{6}{2}\right)^{2}}$$

Divide 6 by 2 to get 3.

$$\sqrt{279+3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{279+9}$$

Add 279 and 9 to get 288.

$$\sqrt{288}$$

Factor 288=12^{2}\times 2. Rewrite the square root of the product \sqrt{12^{2}\times 2} as the product of square roots \sqrt{12^{2}}\sqrt{2}. Take the square root of 12^{2}.

$$12\sqrt{2}$$