Solve =44sqrt{50}-3sqrt{32}+2sqrt{8}

$$= 44 \sqrt { 50 } - 3 \sqrt { 32 } + 2 \sqrt { 8 }$$

Evaluate

$$212\sqrt{2}\approx 299.813275223$$

Solution Steps

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}.

$$44\times 5\sqrt{2}-3\sqrt{32}+2\sqrt{8}$$

Multiply 44 and 5 to get 220.

$$220\sqrt{2}-3\sqrt{32}+2\sqrt{8}$$

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}.

$$220\sqrt{2}-3\times 4\sqrt{2}+2\sqrt{8}$$

Multiply -3 and 4 to get -12.

$$220\sqrt{2}-12\sqrt{2}+2\sqrt{8}$$

Combine 220\sqrt{2} and -12\sqrt{2} to get 208\sqrt{2}.

$$208\sqrt{2}+2\sqrt{8}$$

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}.

$$208\sqrt{2}+2\times 2\sqrt{2}$$

Multiply 2 and 2 to get 4.

$$208\sqrt{2}+4\sqrt{2}$$

Combine 208\sqrt{2} and 4\sqrt{2} to get 212\sqrt{2}.

$$212\sqrt{2}$$