Solve 2sqrt{48}-3sqrt{27}

$$2 \sqrt{ 48 } -3 \sqrt{ 27 }$$

Evaluate

$$-\sqrt{3}\approx -1.732050808$$

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}.

$$2\times 4\sqrt{3}-3\sqrt{27}$$

Multiply 2 and 4 to get 8.

$$8\sqrt{3}-3\sqrt{27}$$

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}.

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

Multiply -3 and 3 to get -9.

$$8\sqrt{3}-9\sqrt{3}$$

Combine 8\sqrt{3} and -9\sqrt{3} to get -\sqrt{3}.

$$-\sqrt{3}$$