Solve 6sqrt{8}-2sqrt{50}

$$6 \sqrt { 8 } - 2 \sqrt { 50 }$$

Evaluate

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

Solution Steps

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}.

$$6\times 2\sqrt{2}-2\sqrt{50}$$

Multiply 6 and 2 to get 12.

$$12\sqrt{2}-2\sqrt{50}$$

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}.

$$12\sqrt{2}-2\times 5\sqrt{2}$$

Multiply -2 and 5 to get -10.

$$12\sqrt{2}-10\sqrt{2}$$

Combine 12\sqrt{2} and -10\sqrt{2} to get 2\sqrt{2}.

$$2\sqrt{2}$$