Question

Is the square root of 225 a rational number?

Answer 1

Explanation:

`\text{The principal square root}:\\\\√(a)=b\iff a^2=b\ \text{for}\ a\geq0\ \text{and}\ b\geq0.\\\\\text{The square root:}\\\\√(a)=b\iff b^2=a\ \text{for}\ a\geq0\\===================`

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

Answer 2

Yes,
`√(225)` is a rational number.

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.

`√(225)`

`√(15^2)`

`15`

Since 15 can be written as
`(15)/(1)`, therefore,
`√(225)` is a rational number.