Solve 3sqrt{3}+6sqrt{12}-5sqrt{75}

$$3 \sqrt { 3 } + 6 \sqrt { 12 } - 5 \sqrt { 75 }$$

Evaluate

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

Solution Steps

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}.

$$3\sqrt{3}+6\times 2\sqrt{3}-5\sqrt{75}$$

Multiply 6 and 2 to get 12.

$$3\sqrt{3}+12\sqrt{3}-5\sqrt{75}$$

Combine 3\sqrt{3} and 12\sqrt{3} to get 15\sqrt{3}.

$$15\sqrt{3}-5\sqrt{75}$$

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}.

$$15\sqrt{3}-5\times 5\sqrt{3}$$

Multiply -5 and 5 to get -25.

$$15\sqrt{3}-25\sqrt{3}$$

Combine 15\sqrt{3} and -25\sqrt{3} to get -10\sqrt{3}.

$$-10\sqrt{3}$$