Is the square root of 25 a whole number?

Yes, the square root of 25 is a whole number. It is 5. But before diving deep into the topic, let’s first understand the meaning of different terms used, such as number, whole number, and square root.

What are Numbers?

Numbers generally also known as numerals are the mathematical values used for, counting, measurements, labelling and measuring fundamental quantities.

Numbers are the mathematical values or figures used for the purpose of measuring or calculating quantities. It is represented by numerals as 2,4,7, etc. Some examples of numbers are integers, whole numbers, natural numbers, rational and irrational numbers, etc.

Types Of Numbers

There are different types of numbers categorized into sets by the number system. The types are described below:

• Natural Numbers: These start from 1 and continue indefinitely (1, 2, 3, 4, 5, …). They represent the basic concept of counting.
• Whole Numbers: Whole numbers include natural numbers along with zero (0, 1, 2, 3, 4, …). They are essential for arithmetic operations.
• Integers: Integers consist of positive and negative whole numbers, including zero (-3, -2, -1, 0, 1, 2, 3, …). They extend the concept of counting to include negative values.
• Rational Numbers: Integers consist of positive and negative whole numbers, including zero (-3, -2, -1, 0, 1, 2, 3, …). They extend the concept of counting to include negative values.
• Irrational Numbers: Irrational numbers cannot be expressed as fractions or ratios. Examples include √2, π (pi), and e. They have non-terminating, non-repeating decimal expansions.
• Real Numbers: Real numbers include both rational and irrational numbers (0, -10, 20, 3.14, …). They form a continuous spectrum on the number line.
• Complex Numbers: Complex numbers involve real and imaginary parts (3 + 2i, -1 – 4i, …). They find applications in fields like engineering and physics.

What is Square Root?

The Square root of a non negative number is a value that when multiplied with itself (squaring ) gives the original number . Symbolically we can say √y =x then y = x²

Ex : √16 = 4 ,√9 =3 , √256=16

Is the square root of 25 a whole number?

Answer:

Yes, the square root of 25 is a whole number. Since, 25 is a perfect square of 5 and after square root being simplified the result would be 5, which is a whole number.

Let’s see the mathematical proof for the statement

Proof:

As we know the value 25 is a perfect square of 5

⇒ 5 × 5=25

Hence, 25 is a perfect square.

Now, a square root of a perfect square can be simplified into counting number 

⇒ √25 = √(5)² = 5

Since the subset of whole numbers include all the positive counting numbers and the value of the square root of 25 is derived to be 5.

The square root of 25 is a whole number.

Conclusion

In summary, the square root of 25 presents us with two valid values: 5 and -5. While both values satisfy the mathematical equation, only 5 aligns with the definition of a whole number. Hence, the square root of 25 is indeed a whole number.

Similar Questions

Question 1: Is the square root of 4 a whole number?

Answer:

Yes, the square root of 4 is a whole number. Since, 4 is a perfect square 2 and after square root being simplified the result would be 2, which is a whole number.

Question 2: Can a square root be a whole number?

Answer:

Yes, if the square root is a perfect square of any real number then, a square root can be a whole number.

Question 3: Is a square root of 25 a rational number?

Answer:

The square root of 25 is equal to 5 as 25 is a perfect square of 5. Hence, as 5 is a integer and can be expressed in the form of p/q root 25 is rational number.

Question 4: Can root 16 be a whole number?

Answer:

Yes, the square root of 16 is a whole number. Since, 16 is a perfect square of 4 and after square root being simplified the result would be 4, which is a whole number.

Question 5 : Are square roots always whole numbers?

Answer :

No, square roots are not always whole numbers. While some square roots result in whole numbers (perfect squares), others are irrational or decimal values. For example, √25 is a whole number (5), but √2 is an irrational number (approximately 1.414).