As the square root of a number r is denoted as √r, we write √25 to express the square root of 25. Before we find the square root of 25, let us first note down a few key things:
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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×r=25, and by definition, the number r will be the square root of 25.
As we know that 25 = 5×5, we have
$\sqrt{25}=\sqrt{5 \times 5}.$
⇒ √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.
This article is written by Dr. T. Mandal, Ph.D in Mathematics. On Mathstoon.com you will find Maths from very basic level to advanced level. Thanks for visiting.