Solve 4sqrt{32}-3sqrt{200}+2sqrt{50}+sqrt{16}2

$$4 \sqrt { 32 } - 3 \sqrt { 200 } + 2 \sqrt { 50 } + \sqrt { 16 } 2$$

Evaluate

$$8-4\sqrt{2}\approx 2.343145751$$

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}.

$$4\times 4\sqrt{2}-3\sqrt{200}+2\sqrt{50}+2\sqrt{16}$$

Multiply 4 and 4 to get 16.

$$16\sqrt{2}-3\sqrt{200}+2\sqrt{50}+2\sqrt{16}$$

Factor 200=10^{2}\times 2. Rewrite the square root of the product \sqrt{10^{2}\times 2} as the product of square roots \sqrt{10^{2}}\sqrt{2}. Take the square root of 10^{2}.

$$16\sqrt{2}-3\times 10\sqrt{2}+2\sqrt{50}+2\sqrt{16}$$

Multiply -3 and 10 to get -30.

$$16\sqrt{2}-30\sqrt{2}+2\sqrt{50}+2\sqrt{16}$$

Combine 16\sqrt{2} and -30\sqrt{2} to get -14\sqrt{2}.

$$-14\sqrt{2}+2\sqrt{50}+2\sqrt{16}$$

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}.

$$-14\sqrt{2}+2\times 5\sqrt{2}+2\sqrt{16}$$

Multiply 2 and 5 to get 10.

$$-14\sqrt{2}+10\sqrt{2}+2\sqrt{16}$$

Combine -14\sqrt{2} and 10\sqrt{2} to get -4\sqrt{2}.

$$-4\sqrt{2}+2\sqrt{16}$$

Calculate the square root of 16 and get 4.

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

Multiply 2 and 4 to get 8.

$$-4\sqrt{2}+8$$