Solve 2sqrt{18}+5sqrt{50}-4sqrt{2}

$$2 \sqrt{ 18 } +5 \sqrt{ 50 } -4 \sqrt{ 2 }$$

Evaluate

$$27\sqrt{2}\approx 38.183766184$$

Solution Steps

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}.

$$2\times 3\sqrt{2}+5\sqrt{50}-4\sqrt{2}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{2}+5\sqrt{50}-4\sqrt{2}$$

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}.

$$6\sqrt{2}+5\times 5\sqrt{2}-4\sqrt{2}$$

Multiply 5 and 5 to get 25.

$$6\sqrt{2}+25\sqrt{2}-4\sqrt{2}$$

Combine 6\sqrt{2} and 25\sqrt{2} to get 31\sqrt{2}.

$$31\sqrt{2}-4\sqrt{2}$$

Combine 31\sqrt{2} and -4\sqrt{2} to get 27\sqrt{2}.

$$27\sqrt{2}$$