Solve sqrt{(3sqrt{5})^2+(4sqrt{5})^2}=

$$\sqrt { ( 3 \sqrt { 5 } ) ^ { 2 } + ( 4 \sqrt { 5 } ) ^ { 2 } } =$$

Evaluate

$$5\sqrt{5}\approx 11.180339887$$

Solution Steps

Expand \left(3\sqrt{5}\right)^{2}.

$$\sqrt{3^{2}\left(\sqrt{5}\right)^{2}+\left(4\sqrt{5}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{9\left(\sqrt{5}\right)^{2}+\left(4\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\sqrt{9\times 5+\left(4\sqrt{5}\right)^{2}}$$

Multiply 9 and 5 to get 45.

$$\sqrt{45+\left(4\sqrt{5}\right)^{2}}$$

Expand \left(4\sqrt{5}\right)^{2}.

$$\sqrt{45+4^{2}\left(\sqrt{5}\right)^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{45+16\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\sqrt{45+16\times 5}$$

Multiply 16 and 5 to get 80.

$$\sqrt{45+80}$$

Add 45 and 80 to get 125.

$$\sqrt{125}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$5\sqrt{5}$$