Solve 8(sqrt{48}-sqrt{12})

$$8 ( \sqrt { 48 } - \sqrt { 12 } )$$

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}.

$$8\left(4\sqrt{3}-\sqrt{12}\right)$$

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}.

$$8\left(4\sqrt{3}-2\sqrt{3}\right)$$

Combine 4\sqrt{3} and -2\sqrt{3} to get 2\sqrt{3}.

$$8\times 2\sqrt{3}$$

Multiply 8 and 2 to get 16.

$$16\sqrt{3}$$