Solve sqrt{27}*2sqrt{20}

$$\sqrt { 27 } \times 2 \sqrt { 20 }$$

Evaluate

$$12\sqrt{15}\approx 46.475800154$$

Solution Steps

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$2\times 3\sqrt{3}\sqrt{20}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{3}\sqrt{20}$$

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}.

$$6\sqrt{3}\times 2\sqrt{5}$$

Multiply 6 and 2 to get 12.

$$12\sqrt{3}\sqrt{5}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$12\sqrt{15}$$