Solve 7^2-sqrt{12}1+8^2-sqrt{22}5

$$7 ^ { 2 } - \sqrt { 12 } 1 + 8 ^ { 2 } - \sqrt { 22 } 5$$

Evaluate

$$113-2\sqrt{3}-5\sqrt{22}\approx 86.083819586$$

Solution Steps

Calculate 7 to the power of 2 and get 49.

$$49-\sqrt{12}+8^{2}-5\sqrt{22}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$49-2\sqrt{3}+8^{2}-5\sqrt{22}$$

Calculate 8 to the power of 2 and get 64.

$$49-2\sqrt{3}+64-5\sqrt{22}$$

Add 49 and 64 to get 113.

$$113-2\sqrt{3}-5\sqrt{22}$$