Solve sqrt{(12sqrt{3})^2+36^2}

$$\sqrt { ( 12 \sqrt { 3 } ) ^ { 2 } + 36 ^ { 2 } }$$

Evaluate

$$24\sqrt{3}\approx 41.569219382$$

Solution Steps

Expand \left(12\sqrt{3}\right)^{2}.

$$\sqrt{12^{2}\left(\sqrt{3}\right)^{2}+36^{2}}$$

Calculate 12 to the power of 2 and get 144.

$$\sqrt{144\left(\sqrt{3}\right)^{2}+36^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{144\times 3+36^{2}}$$

Multiply 144 and 3 to get 432.

$$\sqrt{432+36^{2}}$$

Calculate 36 to the power of 2 and get 1296.

$$\sqrt{432+1296}$$

Add 432 and 1296 to get 1728.

$$\sqrt{1728}$$

Factor 1728=24^{2}\times 3. Rewrite the square root of the product \sqrt{24^{2}\times 3} as the product of square roots \sqrt{24^{2}}\sqrt{3}. Take the square root of 24^{2}.

$$24\sqrt{3}$$