Solve 4sqrt{4}-2sqrt{80}-sqrt{125}

$$4 \sqrt{ 4 } -2 \sqrt{ 80 } - \sqrt{ 125 }$$

Evaluate

$$8-13\sqrt{5}\approx -21.068883707$$

Solution Steps

Calculate the square root of 4 and get 2.

$$4\times 2-2\sqrt{80}-\sqrt{125}$$

Multiply 4 and 2 to get 8.

$$8-2\sqrt{80}-\sqrt{125}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$8-2\times 4\sqrt{5}-\sqrt{125}$$

Multiply -2 and 4 to get -8.

$$8-8\sqrt{5}-\sqrt{125}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$8-8\sqrt{5}-5\sqrt{5}$$

Combine -8\sqrt{5} and -5\sqrt{5} to get -13\sqrt{5}.

$$8-13\sqrt{5}$$