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

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

Evaluate

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

Solution Steps

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

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

Calculate 6 to the power of 2 and get 36.

$$\sqrt{36\left(\sqrt{6}\right)^{2}+\left(6\sqrt{2}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\sqrt{36\times 6+\left(6\sqrt{2}\right)^{2}}$$

Multiply 36 and 6 to get 216.

$$\sqrt{216+\left(6\sqrt{2}\right)^{2}}$$

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

$$\sqrt{216+6^{2}\left(\sqrt{2}\right)^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\sqrt{216+36\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\sqrt{216+36\times 2}$$

Multiply 36 and 2 to get 72.

$$\sqrt{216+72}$$

Add 216 and 72 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}.

$$12\sqrt{2}$$