Solve (1)5sqrt{6}div10sqrt{2}

$$( 1 ) 5 \sqrt { 6 } \div 10 \sqrt { 2 }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

Multiply 5 and 1 to get 5.

$$\frac{5\sqrt{6}}{10}\sqrt{2}$$

Divide 5\sqrt{6} by 10 to get \frac{1}{2}\sqrt{6}.

$$\frac{1}{2}\sqrt{6}\sqrt{2}$$

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

$$\frac{1}{2}\sqrt{2}\sqrt{3}\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{1}{2}\times 2\sqrt{3}$$

Cancel out 2 and 2.

$$\sqrt{3}$$