Solve sqrt{12^2+(3sqrt{2})^2}

$$\sqrt { 12 ^ { 2 } + ( 3 \sqrt { 2 } ) ^ { 2 } }$$

Evaluate

$$9\sqrt{2}\approx 12.727922061$$

Solution Steps

Calculate 12 to the power of 2 and get 144.

$$\sqrt{144+\left(3\sqrt{2}\right)^{2}}$$

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

$$\sqrt{144+3^{2}\left(\sqrt{2}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{144+9\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\sqrt{144+9\times 2}$$

Multiply 9 and 2 to get 18.

$$\sqrt{144+18}$$

Add 144 and 18 to get 162.

$$\sqrt{162}$$

Factor 162=9^{2}\times 2. Rewrite the square root of the product \sqrt{9^{2}\times 2} as the product of square roots \sqrt{9^{2}}\sqrt{2}. Take the square root of 9^{2}.

$$9\sqrt{2}$$