Question

Is the square root of 225 a rational number?

Answer 1

Step-by-step explanation:

$\text{The principal square root}:\\\\\sqrt{a}=b\iff a^2=b\ \text{for}\ a\geq0\ \text{and}\ b\geq0.\\\\\text{The square root:}\\\\\sqrt{a}=b\iff b^2=a\ \text{for}\ a\geq0\\===================$

$\text{If you want the principal square root (arithmetic square root):}\\\\\sqrt{225}=15\ \text{because}\ 15^2=225\\\\\text{If you want square root (algebraic square root):}\\\\\sqrt{225}=\pm15\ \text{because}\ (-15)^2=225\ \text{and}\ 15^2=225$

Answer 2

Answer:

Yes, $\sqrt{225}$ is a rational number.

Step-by-step explanation:

We are asked to determine whether the square root of 225 is a rational number or not.

We know that a number is a rational, when it can be written as a fraction.

Let us find square root of 225.

$\sqrt{225}$

$\sqrt{15^2}$

$15$

Since 15 can be written as $\frac{15}{1}$, therefore, $\sqrt{225}$ is a rational number.