Solve 2sqrt{27}+3sqrt{75}-3sqrt{48}

$$2 \sqrt { 27 } + 3 \sqrt { 75 } - 3 \sqrt { 48 }$$

Evaluate

$$9\sqrt{3}\approx 15.588457268$$

Solution Steps

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}.

$$2\times 3\sqrt{3}+3\sqrt{75}-3\sqrt{48}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{3}+3\sqrt{75}-3\sqrt{48}$$

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}.

$$6\sqrt{3}+3\times 5\sqrt{3}-3\sqrt{48}$$

Multiply 3 and 5 to get 15.

$$6\sqrt{3}+15\sqrt{3}-3\sqrt{48}$$

Combine 6\sqrt{3} and 15\sqrt{3} to get 21\sqrt{3}.

$$21\sqrt{3}-3\sqrt{48}$$

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}.

$$21\sqrt{3}-3\times 4\sqrt{3}$$

Multiply -3 and 4 to get -12.

$$21\sqrt{3}-12\sqrt{3}$$

Combine 21\sqrt{3} and -12\sqrt{3} to get 9\sqrt{3}.

$$9\sqrt{3}$$