Solve sqrt{20}*3sqrt{98}

$$\sqrt { 20 } \times 3 \sqrt { 98 }$$

Evaluate

$$42\sqrt{10}\approx 132.815661727$$

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$3\times 2\sqrt{5}\sqrt{98}$$

Multiply 3 and 2 to get 6.

$$6\sqrt{5}\sqrt{98}$$

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}.

$$6\sqrt{5}\times 7\sqrt{2}$$

Multiply 6 and 7 to get 42.

$$42\sqrt{5}\sqrt{2}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$42\sqrt{10}$$