Solve sqrt{6}*sqrt{27}

$$\sqrt{ 6 } \times \sqrt{ 27 }$$

Evaluate

$$9\sqrt{2}\approx 12.727922061$$

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}.

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

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

Multiply 3 and 3 to get 9.

$$9\sqrt{2}$$