Square root of 100 [Rational or Irrational? Integer?]

The square root of 100 is a number when multiplied by itself will be 100. The square root of 100 is denoted by the symbol √100. In this section, we will learn how to find the value of √100.

The value of the square root of 100 is 10.

If you want to know more about square roots, visit the following pages:

• Basic concepts of square roots
• Properties of square roots

Important Things of Root 100:

• √100 = 10
• 100 is a perfect square.
• √100 is the radical form of square root of 100.
• 100^1/2 is the exponential form of square root of 100.
• The square root of 100 is 10.000 in decimal form.
• Square of 100: 100×100 = 10000
• It is the positive solution of the quadratic equation x²=100.
• If a square has an area of 100 unit², then we use the square root of 100 to find the length of the square.

What is the Square Root of 100?

The value of the square root of 100 is 10. To prove this, we will write 100 as a square of some numbers as 100 is a perfect square. See that 100 is a product of two numbers of 10‘s. So we write

100=10×10=10²

Taking square root on both sides, we have

√100 = √10²

As square root can be written as power 1/2, we get that

√100 = (10²)^1/2 = 10^2×1/2   as we know that (a^m)ⁿ = a^m×n

= 10¹ = 10

So the square root of 100 is 10.  

Is 100 a perfect square number?

We know that √100=10 and 10 is a whole number. This implies that the square root of 100 is also a whole number.

∴ the definition of a perfect square implies that 100 is a perfect square number.

Also Read:

Square root of 49: The square root of 49 is 7.

Square root of 36: The square root of 36 is 6.

Cube root of 125: The cube root of 125 is 5.

Factor of 25: The positive factors of 25 are 1, 5, and 25.

Square root of 100 by Prime Factorization

To find the square root of 100 by the prime factorization method, let us first factorize 100.

As 100 is an even number, it is divisible by 2. So we write

100=2×50.

Again,  50=2×25 and 25=5×5, we obtain that 

100=2×2×5×5 …(∗)

So the above is the prime factorization of 100.

Taking square root on both sides of (∗), we get that

√100 = √(2×2×5×5)

= √(2×2) × √(5×5)

= 2×5  as we know that √a×a=a

= 10 

∴  the value of the square root of 100 is 10. 

Is Square Root of 100 Rational?

We know that a rational number can be written as p/q where p and q are integers with q ≠ 0.

It is known from above that √100=10.

As 10=10/1, we can write 10 as p/q with p=10, q=1≠0.

Thus 10 is a rational number.

⇒ the square root of 100 is also a rational number.

Conclusion: √100 is not an irrational number.

Question Answer on Root 100

Question	Answer
What is the square root of 100?	10 is the square root of 100.
Is the square root of 100 rational or irrational?	As √100=10, the square root of 100 is rational.
What is the positive square root of 100?	The positive square root of 100 is 10.
Is the square root of 100 a whole number?	As √100=10, the square root of 100 is a whole number.
Is square root of 100 an integer?	As √100=10, the square root of 100 is an integer.

 

Key Things about 100

• 100 is a composite even number.
• A square of length 10 unit has the area 100 unit²