Solve 3sqrt{8}+2sqrt{50}-5sqrt{18}

$$3 \sqrt { 8 } + 2 \sqrt { 50 } - 5 \sqrt { 18 }$$

Evaluate

$$\sqrt{2}\approx 1.414213562$$

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}.

$$3\times 2\sqrt{2}+2\sqrt{50}-5\sqrt{18}$$

Multiply 3 and 2 to get 6.

$$6\sqrt{2}+2\sqrt{50}-5\sqrt{18}$$

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}.

$$6\sqrt{2}+2\times 5\sqrt{2}-5\sqrt{18}$$

Multiply 2 and 5 to get 10.

$$6\sqrt{2}+10\sqrt{2}-5\sqrt{18}$$

Combine 6\sqrt{2} and 10\sqrt{2} to get 16\sqrt{2}.

$$16\sqrt{2}-5\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$16\sqrt{2}-5\times 3\sqrt{2}$$

Multiply -5 and 3 to get -15.

$$16\sqrt{2}-15\sqrt{2}$$

Combine 16\sqrt{2} and -15\sqrt{2} to get \sqrt{2}.

$$\sqrt{2}$$