Solve 3sqrt{3}-4sqrt{2}+2sqrt{12}=

$$3 \sqrt{ 3 } -4 \sqrt{ 2 } +2 \sqrt{ 12 } =$$

Evaluate

$$7\sqrt{3}-4\sqrt{2}\approx 6.467501403$$

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}.

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

Multiply 2 and 2 to get 4.

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

Combine 3\sqrt{3} and 4\sqrt{3} to get 7\sqrt{3}.

$$7\sqrt{3}-4\sqrt{2}$$