Solve 5sqrt{75}-2sqrt{108}+5sqrt{12}

$$5 \sqrt { 75 } - 2 \sqrt { 108 } + 5 \sqrt { 12 }$$

Evaluate

$$23\sqrt{3}\approx 39.837168574$$

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}.

$$5\times 5\sqrt{3}-2\sqrt{108}+5\sqrt{12}$$

Multiply 5 and 5 to get 25.

$$25\sqrt{3}-2\sqrt{108}+5\sqrt{12}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$25\sqrt{3}-2\times 6\sqrt{3}+5\sqrt{12}$$

Multiply -2 and 6 to get -12.

$$25\sqrt{3}-12\sqrt{3}+5\sqrt{12}$$

Combine 25\sqrt{3} and -12\sqrt{3} to get 13\sqrt{3}.

$$13\sqrt{3}+5\sqrt{12}$$

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}.

$$13\sqrt{3}+5\times 2\sqrt{3}$$

Multiply 5 and 2 to get 10.

$$13\sqrt{3}+10\sqrt{3}$$

Combine 13\sqrt{3} and 10\sqrt{3} to get 23\sqrt{3}.

$$23\sqrt{3}$$