Solve 6sqrt{48}-sqrt{27}

$$6 \sqrt { 48 } - \sqrt { 27 }$$

Evaluate

$$21\sqrt{3}\approx 36.373066959$$

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}.

$$6\times 4\sqrt{3}-\sqrt{27}$$

Multiply 6 and 4 to get 24.

$$24\sqrt{3}-\sqrt{27}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

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

Combine 24\sqrt{3} and -3\sqrt{3} to get 21\sqrt{3}.

$$21\sqrt{3}$$