Square root of 25

As the square root of a number $r$ is denoted as $\sqrt{r},$ we write $\sqrt{25}$ to express the square root of $25.$ Before we find the square root of $25,$ let us first note down few key things:

The square root of $25$ is $5.$
As $25$ is a perfect square, $\sqrt{25}$ is a whole number.
Square root of $25$ is an integer, so it is a rational number.
$25$ square: $25^2=25 \times 25$ $=625.$
$25^{1/2}$ is the exponential form of square root of $25.$
$\sqrt{25}$ is the radical form or the surd form of the square root of $25.$
Square root of $25$ is $5.00$ in decimal form.

What is the Square Root of 25?

The square root of $25$ is a number $r$ when we multiply by itself will be the number $25.$ In other words, $r \times r=25,$ and by definition, the number $r$ will be the square root of $25.$

As we know that $25=5 \times 5,$ we have

$\sqrt{25}=\sqrt{5 \times 5}.$

⇒ $\sqrt{25}=5.$

So $5$ is the value of the square root of $25.$

Remark: As $(-5) \times (-5)=25,$ by definition of square roots we can conclude the following: $-5$ can also be equal to the square root of $25.$ So from the above discussion it follows that

\[\sqrt{25}=\pm 5.\]

As a result, the square root of $25$ can also be a negative number.


Square Root of 25 by Prime Factorization

The prime factorization method is a very popular method to find the square root of a number. At first, we will factorize $25.$ As the number $25$ has unit digit $5,$ it will be divisible $5.$ So we have $25=5 \times 5.$ Note that $5$ is a prime number, so we cannot factorize further. So finally we obtain the prime factorization of $25$ which is

\[25=5 \times 5.\]

Taking square root on both sides, we get that

$\sqrt{25}=\sqrt{5 \times 5}$

$=5$  $[\because \sqrt{a \times a}=a]$

So the square root of $25$ is $5.$


Is Square Root of 25 Rational?

A rational number has the form p/q where both p and q are integers and q is non-zero. As $\sqrt{25}=\pm 5$ and the numbers $+5$ and $-5$ are rational numbers, we conclude that the square root of $25$ is a rational number.


Is 25 a Perfect Square Number?

Since the square root of $25$ is $5$ and the number $5$ is a whole number, we conclude that:

$25$ is a perfect square number.