Question

Solve root45 * root20 and state what type of number is this (Rational number or irrational number).

Answer 1

Dear Student
Given,

$$\begin{gathered} \left(\sqrt{20}\right)\times \left(\sqrt{45}\right) \\ =\left(\sqrt{5\times 4}\right)\times \left(\sqrt{5\times 9}\right) \\ =\left(\sqrt{5}\right)\times \left(\sqrt{4}\right)\times \left(\sqrt{5}\right)\times \left(\sqrt{9}\right) \\ ={\left(\sqrt{5}\right)}^2\times \left(\sqrt{4}\right)\times \left(\sqrt{9}\right) \\ =5\times 2\times 3 \\ =5\times 6 \\ =30(=\frac{30}{1}=\frac{p}{q})Hence,Rational \end{gathered}$$

Regards