Solve sqrt{90div4}

$$\sqrt{ 90 \div 4 }$$

Evaluate

$$\frac{3\sqrt{10}}{2}\approx 4.74341649$$

Solution Steps

Reduce the fraction \frac{90}{4} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{45}{2}}$$

Rewrite the square root of the division \sqrt{\frac{45}{2}} as the division of square roots \frac{\sqrt{45}}{\sqrt{2}}.

$$\frac{\sqrt{45}}{\sqrt{2}}$$

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}.

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

Rationalize the denominator of \frac{3\sqrt{5}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{3\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{3\sqrt{10}}{2}$$