Solve sqrt{(2sqrt{15})^2+(4sqrt{5})^2}

$$\sqrt { ( 2 \sqrt { 15 } ) ^ { 2 } + ( 4 \sqrt { 5 } ) ^ { 2 } }$$

Evaluate

$$2\sqrt{35}\approx 11.832159566$$

Solution Steps

Expand \left(2\sqrt{15}\right)^{2}.

$$\sqrt{2^{2}\left(\sqrt{15}\right)^{2}+\left(4\sqrt{5}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{4\left(\sqrt{15}\right)^{2}+\left(4\sqrt{5}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\sqrt{4\times 15+\left(4\sqrt{5}\right)^{2}}$$

Multiply 4 and 15 to get 60.

$$\sqrt{60+\left(4\sqrt{5}\right)^{2}}$$

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

$$\sqrt{60+4^{2}\left(\sqrt{5}\right)^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{60+16\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\sqrt{60+16\times 5}$$

Multiply 16 and 5 to get 80.

$$\sqrt{60+80}$$

Add 60 and 80 to get 140.

$$\sqrt{140}$$

Factor 140=2^{2}\times 35. Rewrite the square root of the product \sqrt{2^{2}\times 35} as the product of square roots \sqrt{2^{2}}\sqrt{35}. Take the square root of 2^{2}.

$$2\sqrt{35}$$