Solve (1)3sqrt{8}+2sqrt{32}-sqrt{50}

$$( 1 ) 3 \sqrt { 8 } + 2 \sqrt { 32 } - \sqrt { 50 }$$

Evaluate

$$9\sqrt{2}\approx 12.727922061$$

Solution Steps

Multiply 3 and 1 to get 3.

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

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}.

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

Multiply 3 and 2 to get 6.

$$6\sqrt{2}+2\sqrt{32}-\sqrt{50}$$

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}.

$$6\sqrt{2}+2\times 4\sqrt{2}-\sqrt{50}$$

Multiply 2 and 4 to get 8.

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

Combine 6\sqrt{2} and 8\sqrt{2} to get 14\sqrt{2}.

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

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}.

$$14\sqrt{2}-5\sqrt{2}$$

Combine 14\sqrt{2} and -5\sqrt{2} to get 9\sqrt{2}.

$$9\sqrt{2}$$