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, an expert in Mathematics (PhD). On Mathstoon.com you will find Maths from very basic level to advanced level. Thanks for visiting.