Solve 2sqrt{50}-2sqrt{32}

$$2 \sqrt{ 50 } -2 \sqrt{ 32 }$$

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

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}.

$$2\times 5\sqrt{2}-2\sqrt{32}$$

Multiply 2 and 5 to get 10.

$$10\sqrt{2}-2\sqrt{32}$$

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}.

$$10\sqrt{2}-2\times 4\sqrt{2}$$

Multiply -2 and 4 to get -8.

$$10\sqrt{2}-8\sqrt{2}$$

Combine 10\sqrt{2} and -8\sqrt{2} to get 2\sqrt{2}.

$$2\sqrt{2}$$