Solve sqrt{30}*sqrt{40}

$$\sqrt{ 30 } \times \sqrt{ 40 }$$

Evaluate

$$20\sqrt{3}\approx 34.641016151$$

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}.

$$\sqrt{30}\times 2\sqrt{10}$$

Factor 30=10\times 3. Rewrite the square root of the product \sqrt{10\times 3} as the product of square roots \sqrt{10}\sqrt{3}.

$$\sqrt{10}\sqrt{3}\times 2\sqrt{10}$$

Multiply \sqrt{10} and \sqrt{10} to get 10.

$$10\times 2\sqrt{3}$$

Multiply 10 and 2 to get 20.

$$20\sqrt{3}$$