Solve sqrt{30*20}*sqrt{60}

$$\sqrt{ 30 \cdot 20 } \times \sqrt{ 60 }$$

Evaluate

$$60\sqrt{10}\approx 189.73665961$$

Solution Steps

Multiply 30 and 20 to get 600.

$$\sqrt{600}\sqrt{60}$$

Factor 600=10^{2}\times 6. Rewrite the square root of the product \sqrt{10^{2}\times 6} as the product of square roots \sqrt{10^{2}}\sqrt{6}. Take the square root of 10^{2}.

$$10\sqrt{6}\sqrt{60}$$

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}.

$$10\sqrt{6}\times 2\sqrt{15}$$

Multiply 10 and 2 to get 20.

$$20\sqrt{6}\sqrt{15}$$

To multiply \sqrt{6} and \sqrt{15}, multiply the numbers under the square root.

$$20\sqrt{90}$$

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

$$20\times 3\sqrt{10}$$

Multiply 20 and 3 to get 60.

$$60\sqrt{10}$$