Solve 12sqrt{12}-sqrt{75}

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

Evaluate

$$19\sqrt{3}\approx 32.908965344$$

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}.

$$12\times 2\sqrt{3}-\sqrt{75}$$

Multiply 12 and 2 to get 24.

$$24\sqrt{3}-\sqrt{75}$$

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}.

$$24\sqrt{3}-5\sqrt{3}$$

Combine 24\sqrt{3} and -5\sqrt{3} to get 19\sqrt{3}.

$$19\sqrt{3}$$