Q:

Is the square root of 225 a rational number?

Accepted Solution

A:
Step-by-step explanation:[tex]\text{The principal square root}:\\\\\sqrt{a}=b\iff a^2=b\ \text{for}\ a\geq0\ \text{and}\ b\geq0.\\\\\text{The square root:}\\\\\sqrt{a}=b\iff b^2=a\ \text{for}\ a\geq0\\===================[/tex][tex]\text{If you want the principal square root (arithmetic square root):}\\\\\sqrt{225}=15\ \text{because}\ 15^2=225\\\\\text{If you want square root (algebraic square root):}\\\\\sqrt{225}=\pm15\ \text{because}\ (-15)^2=225\ \text{and}\ 15^2=225[/tex]