Solve sqrt{(6sqrt{5})^2+(3sqrt{5})^2}

$$\sqrt { ( 6 \sqrt { 5 } ) ^ { 2 } + ( 3 \sqrt { 5 } ) ^ { 2 } }$$

Evaluate

$$15$$

Solution Steps

Expand \left(6\sqrt{5}\right)^{2}.

$$\sqrt{6^{2}\left(\sqrt{5}\right)^{2}+\left(3\sqrt{5}\right)^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\sqrt{36\left(\sqrt{5}\right)^{2}+\left(3\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\sqrt{36\times 5+\left(3\sqrt{5}\right)^{2}}$$

Multiply 36 and 5 to get 180.

$$\sqrt{180+\left(3\sqrt{5}\right)^{2}}$$

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

$$\sqrt{180+3^{2}\left(\sqrt{5}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{180+9\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\sqrt{180+9\times 5}$$

Multiply 9 and 5 to get 45.

$$\sqrt{180+45}$$

Add 180 and 45 to get 225.

$$\sqrt{225}$$

Calculate the square root of 225 and get 15.

$$15$$

Factor

$$3\times 5$$