Solve -5sqrt{18}divsqrt{50}

$$- 5 \sqrt { 18 } \div \sqrt { 50 }$$

Evaluate

$$-3$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{-5\times 3\sqrt{2}}{\sqrt{50}}$$

Multiply -5 and 3 to get -15.

$$\frac{-15\sqrt{2}}{\sqrt{50}}$$

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}.

$$\frac{-15\sqrt{2}}{5\sqrt{2}}$$

Cancel out 5\sqrt{2} in both numerator and denominator.

$$-3$$

Factor

$$-3$$