What’s the square root of 25 in simplest radical form
The Correct Answer and Explanation is :
The square root of 25 is 5. In simplest radical form, this can be expressed as ( \sqrt{25} = 5 ).
Explanation:
To understand why the square root of 25 equals 5, it’s essential to grasp the concept of square roots. The square root of a number ( x ) is another number ( y ) such that when ( y ) is multiplied by itself (i.e., ( y \times y ) or ( y^2 )), the result is ( x ). In mathematical terms, this is expressed as:
[
\sqrt{x} = y \quad \text{if and only if} \quad y^2 = x
]
For the case of 25, we are looking for a number that, when squared, equals 25. We can identify that:
[
5 \times 5 = 25
]
Therefore, we can conclude that the square root of 25 is 5.
In terms of radical notation, the square root is represented by the radical symbol ( \sqrt{} ). When simplifying square roots, we look for perfect squares—numbers that can be expressed as the product of an integer multiplied by itself. The number 25 is a perfect square since it can be written as ( 5^2 ). Thus, the square root of a perfect square is simply the base number, which in this case is 5.
When dealing with non-perfect squares, we might end up with an expression in radical form, like ( \sqrt{2} ) or ( \sqrt{3} ), which cannot be simplified to a whole number. However, since 25 is a perfect square, its square root is expressed in simplest form as the integer 5 without any radical notation remaining.
In conclusion, the square root of 25 is ( \sqrt{25} = 5 ), and this result is presented in its simplest radical form as an integer.