Solve 2sqrt{98}-4sqrt{18}

$$2 \sqrt { 98 } - 4 \sqrt { 18 }$$

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$2\times 7\sqrt{2}-4\sqrt{18}$$

Multiply 2 and 7 to get 14.

$$14\sqrt{2}-4\sqrt{18}$$

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}.

$$14\sqrt{2}-4\times 3\sqrt{2}$$

Multiply -4 and 3 to get -12.

$$14\sqrt{2}-12\sqrt{2}$$

Combine 14\sqrt{2} and -12\sqrt{2} to get 2\sqrt{2}.

$$2\sqrt{2}$$