Solve 6sqrt{75}-sqrt{12}

$$6 \sqrt { 75 } - \sqrt { 12 }$$

Evaluate

$$28\sqrt{3}\approx 48.497422612$$

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}.

$$6\times 5\sqrt{3}-\sqrt{12}$$

Multiply 6 and 5 to get 30.

$$30\sqrt{3}-\sqrt{12}$$

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}.

$$30\sqrt{3}-2\sqrt{3}$$

Combine 30\sqrt{3} and -2\sqrt{3} to get 28\sqrt{3}.

$$28\sqrt{3}$$