Question

question determine if √72 is rational or irrational and give a reason for your answer. answer attempt 1 out of 5 the number √72 is because rational irrational

Explanation:

Step1: Simplify the square - root

We simplify $\sqrt{72}=\sqrt{36\times2}$.
Using the property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ ($a = 36$, $b = 2$), we get $\sqrt{72}=\sqrt{36}\times\sqrt{2}=6\sqrt{2}$.

Step2: Recall the definition of rational and irrational numbers

A rational number can be written as $\frac{p}{q}$ where $p,q\in\mathbb{Z}$ and $q
eq0$. $\sqrt{2}$ is an irrational number (it cannot be written as a fraction of two integers). Since $\sqrt{72}=6\sqrt{2}$, and it is a non - zero multiple of an irrational number, it is also irrational.

Answer:

irrational