Question

exercises simplify the quotient. 51. $\frac{sqrt{27}}{sqrt{45}}$

Explanation:

Step1: Combine radicals into one

$\frac{\sqrt{27}}{\sqrt{45}} = \sqrt{\frac{27}{45}}$

Step2: Simplify the fraction inside

$\sqrt{\frac{27}{45}} = \sqrt{\frac{3}{5}}$

Step3: Rationalize the denominator

$\sqrt{\frac{3}{5}} = \frac{\sqrt{3}}{\sqrt{5}} = \frac{\sqrt{3} \times \sqrt{5}}{\sqrt{5} \times \sqrt{5}} = \frac{\sqrt{15}}{5}$

Answer:

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