Solve 2(sqrt{64}-sqrt{288})-(5-2sqrt{2})^2+sqrt{132}=

$$2 ( \sqrt { 64 } - \sqrt { 288 } ) - ( 5 - 2 \sqrt { 2 } ) ^ { 2 } + \sqrt { 132 } =$$

Evaluate

$$2\sqrt{33}-4\sqrt{2}-17\approx -11.167728956$$

Solution Steps

Calculate the square root of 64 and get 8.

$$2\left(8-\sqrt{288}\right)-\left(5-2\sqrt{2}\right)^{2}+\sqrt{132}$$

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}.

$$2\left(8-12\sqrt{2}\right)-\left(5-2\sqrt{2}\right)^{2}+\sqrt{132}$$

Use the distributive property to multiply 2 by 8-12\sqrt{2}.

$$16-24\sqrt{2}-\left(5-2\sqrt{2}\right)^{2}+\sqrt{132}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5-2\sqrt{2}\right)^{2}.

$$16-24\sqrt{2}-\left(25-20\sqrt{2}+4\left(\sqrt{2}\right)^{2}\right)+\sqrt{132}$$

The square of \sqrt{2} is 2.

$$16-24\sqrt{2}-\left(25-20\sqrt{2}+4\times 2\right)+\sqrt{132}$$

Multiply 4 and 2 to get 8.

$$16-24\sqrt{2}-\left(25-20\sqrt{2}+8\right)+\sqrt{132}$$

Add 25 and 8 to get 33.

$$16-24\sqrt{2}-\left(33-20\sqrt{2}\right)+\sqrt{132}$$

To find the opposite of 33-20\sqrt{2}, find the opposite of each term.

$$16-24\sqrt{2}-33+20\sqrt{2}+\sqrt{132}$$

Subtract 33 from 16 to get -17.

$$-17-24\sqrt{2}+20\sqrt{2}+\sqrt{132}$$

Combine -24\sqrt{2} and 20\sqrt{2} to get -4\sqrt{2}.

$$-17-4\sqrt{2}+\sqrt{132}$$

Factor 132=2^{2}\times 33. Rewrite the square root of the product \sqrt{2^{2}\times 33} as the product of square roots \sqrt{2^{2}}\sqrt{33}. Take the square root of 2^{2}.

$$-17-4\sqrt{2}+2\sqrt{33}$$