Question

question
determine if \\(\sqrt{72}\\) is rational or irrational and give a reason for your answer.
answer attempt 1 out of 2
the number \\(\sqrt{72}\\) is because

Explanation:

Step1: Simplify $\sqrt{72}$

Factor 72: $72 = 36\times2$. So, $\sqrt{72}=\sqrt{36\times2}$. Using the property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (for $a\geq0,b\geq0$), we get $\sqrt{36\times2}=\sqrt{36}\times\sqrt{2}=6\sqrt{2}$.

Step2: Determine if $6\sqrt{2}$ is rational or irrational

A rational number can be expressed as $\frac{p}{q}$ where $p,q$ are integers and $q
eq0$. $\sqrt{2}$ is irrational (it cannot be written as a fraction of integers). Multiplying a non - zero rational number (6) by an irrational number ($\sqrt{2}$) gives an irrational number. So, $6\sqrt{2}$ (which is $\sqrt{72}$) is irrational.

Answer:

The number $\sqrt{72}$ is irrational because $\sqrt{72} = 6\sqrt{2}$, and since $\sqrt{2}$ is irrational, multiplying it by the rational number 6 results in an irrational number (or because 72 is not a perfect square, so its square root is irrational).