Solve 3sqrt{50}-2sqrt{32}

$$3 \sqrt { 50 } - 2 \sqrt { 32 }$$

Evaluate

$$7\sqrt{2}\approx 9.899494937$$

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}.

$$3\times 5\sqrt{2}-2\sqrt{32}$$

Multiply 3 and 5 to get 15.

$$15\sqrt{2}-2\sqrt{32}$$

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}.

$$15\sqrt{2}-2\times 4\sqrt{2}$$

Multiply -2 and 4 to get -8.

$$15\sqrt{2}-8\sqrt{2}$$

Combine 15\sqrt{2} and -8\sqrt{2} to get 7\sqrt{2}.

$$7\sqrt{2}$$