Solve 4sqrt{32}+sqrt{50}-3sqrt{8}

$$4 \sqrt { 32 } + \sqrt { 50 } - 3 \sqrt { 8 }$$

Evaluate

$$15\sqrt{2}\approx 21.213203436$$

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}.

$$4\times 4\sqrt{2}+\sqrt{50}-3\sqrt{8}$$

Multiply 4 and 4 to get 16.

$$16\sqrt{2}+\sqrt{50}-3\sqrt{8}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$16\sqrt{2}+5\sqrt{2}-3\sqrt{8}$$

Combine 16\sqrt{2} and 5\sqrt{2} to get 21\sqrt{2}.

$$21\sqrt{2}-3\sqrt{8}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$21\sqrt{2}-3\times 2\sqrt{2}$$

Multiply -3 and 2 to get -6.

$$21\sqrt{2}-6\sqrt{2}$$

Combine 21\sqrt{2} and -6\sqrt{2} to get 15\sqrt{2}.

$$15\sqrt{2}$$