Solve 2sqrt{98}*sqrt{32}

$$2 \sqrt { 98 } \times \sqrt { 32 }$$

Evaluate

$$112$$

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}.

$$2\times 7\sqrt{2}\sqrt{32}$$

Multiply 2 and 7 to get 14.

$$14\sqrt{2}\sqrt{32}$$

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}.

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

Multiply 14 and 4 to get 56.

$$56\sqrt{2}\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$56\times 2$$

Multiply 56 and 2 to get 112.

$$112$$

Factor

$$2^{4}\times 7$$