Solve 2sqrt{3}+5sqrt{12}-3sqrt{27}=

$$2 \sqrt{ 3 } +5 \sqrt{ 12 } -3 \sqrt{ 27 } =$$

Evaluate

$$3\sqrt{3}\approx 5.196152423$$

Solution Steps

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}.

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

Multiply 5 and 2 to get 10.

$$2\sqrt{3}+10\sqrt{3}-3\sqrt{27}$$

Combine 2\sqrt{3} and 10\sqrt{3} to get 12\sqrt{3}.

$$12\sqrt{3}-3\sqrt{27}$$

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}.

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

Multiply -3 and 3 to get -9.

$$12\sqrt{3}-9\sqrt{3}$$

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

$$3\sqrt{3}$$