Solve 3sqrt{2}-2sqrt{12}+3sqrt{45}-2sqrt{3}

$$3 \sqrt { 2 } - 2 \sqrt { 12 } + 3 \sqrt { 45 } - 2 \sqrt { 3 }$$

Evaluate

$$3\left(\sqrt{2}+3\sqrt{5}-2\sqrt{3}\right)\approx 13.974947639$$

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}.

$$3\sqrt{2}-2\times 2\sqrt{3}+3\sqrt{45}-2\sqrt{3}$$

Multiply -2 and 2 to get -4.

$$3\sqrt{2}-4\sqrt{3}+3\sqrt{45}-2\sqrt{3}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

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

Multiply 3 and 3 to get 9.

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

Combine -4\sqrt{3} and -2\sqrt{3} to get -6\sqrt{3}.

$$3\sqrt{2}-6\sqrt{3}+9\sqrt{5}$$