Solve 3sqrt{27}+5sqrt{48}+sqrt{75}-2sqrt{12}=

$$3 \sqrt { 27 } + 5 \sqrt { 48 } + \sqrt { 75 } - 2 \sqrt { 12 } =$$

Evaluate

$$30\sqrt{3}\approx 51.961524227$$

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}.

$$3\times 3\sqrt{3}+5\sqrt{48}+\sqrt{75}-2\sqrt{12}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{3}+5\sqrt{48}+\sqrt{75}-2\sqrt{12}$$

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}.

$$9\sqrt{3}+5\times 4\sqrt{3}+\sqrt{75}-2\sqrt{12}$$

Multiply 5 and 4 to get 20.

$$9\sqrt{3}+20\sqrt{3}+\sqrt{75}-2\sqrt{12}$$

Combine 9\sqrt{3} and 20\sqrt{3} to get 29\sqrt{3}.

$$29\sqrt{3}+\sqrt{75}-2\sqrt{12}$$

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}.

$$29\sqrt{3}+5\sqrt{3}-2\sqrt{12}$$

Combine 29\sqrt{3} and 5\sqrt{3} to get 34\sqrt{3}.

$$34\sqrt{3}-2\sqrt{12}$$

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}.

$$34\sqrt{3}-2\times 2\sqrt{3}$$

Multiply -2 and 2 to get -4.

$$34\sqrt{3}-4\sqrt{3}$$

Combine 34\sqrt{3} and -4\sqrt{3} to get 30\sqrt{3}.

$$30\sqrt{3}$$