Solve sqrt{99/4}

$$\sqrt { 9 \frac { 9 } { 4 } }$$

Evaluate

$$\frac{3\sqrt{5}}{2}\approx 3.354101966$$

Solution Steps

Multiply 9 and 4 to get 36.

$$\sqrt{\frac{36+9}{4}}$$

Add 36 and 9 to get 45.

$$\sqrt{\frac{45}{4}}$$

Rewrite the square root of the division \sqrt{\frac{45}{4}} as the division of square roots \frac{\sqrt{45}}{\sqrt{4}}.

$$\frac{\sqrt{45}}{\sqrt{4}}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$\frac{3\sqrt{5}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

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