Solve 5sqrt{20}-2sqrt{75}+4sqrt{12}

$$5 \sqrt { 20 } - 2 \sqrt { 75 } + 4 \sqrt { 12 }$$

Evaluate

$$2\left(5\sqrt{5}-\sqrt{3}\right)\approx 18.89657816$$

Solution Steps

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}.

$$5\times 2\sqrt{5}-2\sqrt{75}+4\sqrt{12}$$

Multiply 5 and 2 to get 10.

$$10\sqrt{5}-2\sqrt{75}+4\sqrt{12}$$

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}.

$$10\sqrt{5}-2\times 5\sqrt{3}+4\sqrt{12}$$

Multiply -2 and 5 to get -10.

$$10\sqrt{5}-10\sqrt{3}+4\sqrt{12}$$

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}.

$$10\sqrt{5}-10\sqrt{3}+4\times 2\sqrt{3}$$

Multiply 4 and 2 to get 8.

$$10\sqrt{5}-10\sqrt{3}+8\sqrt{3}$$

Combine -10\sqrt{3} and 8\sqrt{3} to get -2\sqrt{3}.

$$10\sqrt{5}-2\sqrt{3}$$