Solve sqrt{6}sqrt{40}=

$$\sqrt { 6 } \sqrt { 40 } =$$

Evaluate

$$4\sqrt{15}\approx 15.491933385$$

Solution Steps

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$\sqrt{6}\times 2\sqrt{10}$$

To multiply \sqrt{6} and \sqrt{10}, multiply the numbers under the square root.

$$\sqrt{60}\times 2$$

Factor 60=2^{2}\times 15. Rewrite the square root of the product \sqrt{2^{2}\times 15} as the product of square roots \sqrt{2^{2}}\sqrt{15}. Take the square root of 2^{2}.

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

Multiply 2 and 2 to get 4.

$$4\sqrt{15}$$