Solve 7sqrt{48}-6sqrt{12}

$$7 \sqrt { 48 } - 6 \sqrt { 12 }$$

Evaluate

$$16\sqrt{3}\approx 27.712812921$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$7\times 4\sqrt{3}-6\sqrt{12}$$

Multiply 7 and 4 to get 28.

$$28\sqrt{3}-6\sqrt{12}$$

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}.

$$28\sqrt{3}-6\times 2\sqrt{3}$$

Multiply -6 and 2 to get -12.

$$28\sqrt{3}-12\sqrt{3}$$

Combine 28\sqrt{3} and -12\sqrt{3} to get 16\sqrt{3}.

$$16\sqrt{3}$$