Solve sqrt{27}sqrt{50}div6

$$\sqrt{ 27 } \sqrt{ 50 } \div 6$$

Evaluate

$$\frac{5\sqrt{6}}{2}\approx 6.123724357$$

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}.

$$\frac{3\sqrt{3}\sqrt{50}}{6}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

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

Multiply 3 and 5 to get 15.

$$\frac{15\sqrt{3}\sqrt{2}}{6}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{15\sqrt{6}}{6}$$

Divide 15\sqrt{6} by 6 to get \frac{5}{2}\sqrt{6}.

$$\frac{5}{2}\sqrt{6}$$