Solve sqrt{(2)(10)}-sqrt{2^2+8(2)}

$$\sqrt{ (2)(10) } - \sqrt{ { 2 }^{ 2 } +8(2) }$$

Evaluate

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Solution Steps

Multiply 2 and 10 to get 20.

$$\sqrt{20}-\sqrt{2^{2}+8\times 2}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$2\sqrt{5}-\sqrt{2^{2}+8\times 2}$$

Calculate 2 to the power of 2 and get 4.

$$2\sqrt{5}-\sqrt{4+8\times 2}$$

Multiply 8 and 2 to get 16.

$$2\sqrt{5}-\sqrt{4+16}$$

Add 4 and 16 to get 20.

$$2\sqrt{5}-\sqrt{20}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$2\sqrt{5}-2\sqrt{5}$$

Combine 2\sqrt{5} and -2\sqrt{5} to get 0.

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Factor

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