Solve 5sqrt{18}-4sqrt{8}

$$5 \sqrt { 18 } - 4 \sqrt { 8 }$$

Evaluate

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

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}.

$$5\times 3\sqrt{2}-4\sqrt{8}$$

Multiply 5 and 3 to get 15.

$$15\sqrt{2}-4\sqrt{8}$$

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}.

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

Multiply -4 and 2 to get -8.

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

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

$$7\sqrt{2}$$