Solve 3sqrt{32}-34sqrt{18}+5sqrt{2}

$$3 \sqrt { 32 } - 34 \sqrt { 18 } + 5 \sqrt { 2 }$$

Evaluate

$$-85\sqrt{2}\approx -120.208152802$$

Solution Steps

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}.

$$3\times 4\sqrt{2}-34\sqrt{18}+5\sqrt{2}$$

Multiply 3 and 4 to get 12.

$$12\sqrt{2}-34\sqrt{18}+5\sqrt{2}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$12\sqrt{2}-34\times 3\sqrt{2}+5\sqrt{2}$$

Multiply -34 and 3 to get -102.

$$12\sqrt{2}-102\sqrt{2}+5\sqrt{2}$$

Combine 12\sqrt{2} and -102\sqrt{2} to get -90\sqrt{2}.

$$-90\sqrt{2}+5\sqrt{2}$$

Combine -90\sqrt{2} and 5\sqrt{2} to get -85\sqrt{2}.

$$-85\sqrt{2}$$