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

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

Evaluate

$$5\sqrt{3}\approx 8.660254038$$

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}.

$$4\sqrt{3}+2\sqrt{75}-3\sqrt{27}$$

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}.

$$4\sqrt{3}+2\times 5\sqrt{3}-3\sqrt{27}$$

Multiply 2 and 5 to get 10.

$$4\sqrt{3}+10\sqrt{3}-3\sqrt{27}$$

Combine 4\sqrt{3} and 10\sqrt{3} to get 14\sqrt{3}.

$$14\sqrt{3}-3\sqrt{27}$$

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}.

$$14\sqrt{3}-3\times 3\sqrt{3}$$

Multiply -3 and 3 to get -9.

$$14\sqrt{3}-9\sqrt{3}$$

Combine 14\sqrt{3} and -9\sqrt{3} to get 5\sqrt{3}.

$$5\sqrt{3}$$