Solve 7sqrt{12}+2sqrt{2}-9sqrt{3}+5sqrt{32}

$$7 \sqrt{ 12 } +2 \sqrt{ 2 } -9 \sqrt{ 3 } +5 \sqrt{ 32 }$$

Evaluate

$$5\sqrt{3}+22\sqrt{2}\approx 39.77295241$$

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}.

$$7\times 2\sqrt{3}+2\sqrt{2}-9\sqrt{3}+5\sqrt{32}$$

Multiply 7 and 2 to get 14.

$$14\sqrt{3}+2\sqrt{2}-9\sqrt{3}+5\sqrt{32}$$

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

$$5\sqrt{3}+2\sqrt{2}+5\sqrt{32}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

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

Multiply 5 and 4 to get 20.

$$5\sqrt{3}+2\sqrt{2}+20\sqrt{2}$$

Combine 2\sqrt{2} and 20\sqrt{2} to get 22\sqrt{2}.

$$5\sqrt{3}+22\sqrt{2}$$