Solve 2sqrt{75}+3sqrt{20}-(sqrt{125}+sqrt{5})

$$2 \sqrt { 75 } + 3 \sqrt { 20 } - ( \sqrt { 125 } + \sqrt { 5 } )$$

Evaluate

$$10\sqrt{3}\approx 17.320508076$$

Solution Steps

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$2\times 5\sqrt{3}+3\sqrt{20}-\left(\sqrt{125}+\sqrt{5}\right)$$

Multiply 2 and 5 to get 10.

$$10\sqrt{3}+3\sqrt{20}-\left(\sqrt{125}+\sqrt{5}\right)$$

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}.

$$10\sqrt{3}+3\times 2\sqrt{5}-\left(\sqrt{125}+\sqrt{5}\right)$$

Multiply 3 and 2 to get 6.

$$10\sqrt{3}+6\sqrt{5}-\left(\sqrt{125}+\sqrt{5}\right)$$

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}.

$$10\sqrt{3}+6\sqrt{5}-\left(5\sqrt{5}+\sqrt{5}\right)$$

Combine 5\sqrt{5} and \sqrt{5} to get 6\sqrt{5}.

$$10\sqrt{3}+6\sqrt{5}-6\sqrt{5}$$

Combine 6\sqrt{5} and -6\sqrt{5} to get 0.

$$10\sqrt{3}$$