Solve frac{sqrt{18}}{4}divfrac{sqrt{25}}{10}

$$\frac { \sqrt { 18 } } { 4 } \div \frac { \sqrt { 25 } } { 10 }$$

Evaluate

$$\frac{3\sqrt{2}}{2}\approx 2.121320344$$

Solution Steps

Divide \frac{\sqrt{18}}{4} by \frac{\sqrt{25}}{10} by multiplying \frac{\sqrt{18}}{4} by the reciprocal of \frac{\sqrt{25}}{10}.

$$\frac{\sqrt{18}\times 10}{4\sqrt{25}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5\sqrt{18}}{2\sqrt{25}}$$

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}.

$$\frac{5\times 3\sqrt{2}}{2\sqrt{25}}$$

Multiply 5 and 3 to get 15.

$$\frac{15\sqrt{2}}{2\sqrt{25}}$$

Calculate the square root of 25 and get 5.

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

Multiply 2 and 5 to get 10.

$$\frac{15\sqrt{2}}{10}$$

Divide 15\sqrt{2} by 10 to get \frac{3}{2}\sqrt{2}.

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