Square root of 25

Introduction to the Square Root of 25

The square root of 25 is a mathematical expression denoting a value that, when multiplied by itself, equals 25. The result of the square root of 25 is 5. This is because 5 × 5 = 25. Understanding how to compute square roots is fundamental in mathematics and has various applications in science, engineering, and everyday problem-solving.

How to Calculate the Square Root of 25

Calculating the square root of a number involves finding a value that, when squared, returns the original number. In the case of 25, we are looking for a number x such that x² = 25.

One method to determine the square root is through factorization. First, we perform prime factorization of 25. The number 25 can be expressed as a product of its prime factors: 5 × 5. Each pair of identical factors, in this case, a pair of 5s, corresponds to a number that can be extracted from the square root. Therefore, the square root of 25 is 5.

Another approach is to use the method of repeated subtraction, which is more intuitive but less efficient for larger numbers. Here, we subtract consecutive odd numbers starting from 1 from 25 until we reach zero. The number of times we can subtract is the square root:

25 - 1 = 24
24 - 3 = 21
21 - 5 = 16
16 - 7 = 9
9 - 9 = 0

Since we subtracted five odd numbers, the square root of 25 is again confirmed as 5.

Rational or Irrational?

The square root of 25 is a rational number. Rational numbers are numbers that can be expressed as a fraction of two integers. In this case, the square root of 25 is 5, which can be expressed as 5/1. Since it can be written as a simple fraction, it is a rational number.

Common Questions and Answers

Q1: Is the square root of 25 always positive?

A: The principal square root of 25 is positive and equals 5. However, mathematically, both 5 and -5 are square roots of 25 because (-5) × (-5) = 25 as well.

Q2: Can square roots be negative?

A: While the term "square root" typically refers to the principal (positive) root, negative numbers can also satisfy the squaring equation. In the context of real numbers, square roots are generally considered to be non-negative.

Q3: How can I verify the square root of a number?

A: To verify the square root of a number, simply multiply the square root by itself. If the result equals the original number, your calculation is correct. For example, verifying 5 as the square root of 25 involves calculating 5 × 5, which equals 25.