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Square Root

What Is the Square Root of 900? How to Find the Square Root of 900?

Written by Prerit Jain

Updated on: 12 Aug 2023

What Is the Square Root of 900? How to Find the Square Root of 900?

What Is the Square Root of 900? How to Find the Square Root of 900?

The square root of 900 is 30. When the square of the number gives the original value that is the square root of the number, or the inversion of the square root is just the squaring of the number. When the number 30 is squared we get 900.

Check whether the given number is the perfect square number or not. When the number is a perfect square we can find the square of the perfect number by long division, prime factorization, and repeated subtraction.

For a larger square number like 900 repeated subtraction is extremely time-consuming hence long division and prime factorization methods are preferred. The long division method is used to find the square root of imperfect square values. 

Square root value of 900

When the number is multiplied by itself it should be 900 and was expressed as √900
√900 = √(number× number)
The number when multiplied twice that gives 900 is 30
√900 = 30×30
√900 = √(30)2
By canceling the squares we get
√900 = 30.

Methods to find the square root of 900

  • Prime factorization method
  • Long division method

Prime factorization method

It is one of the easiest and simplest methods to find the square root of a number:

  • Step 1: Find the prime factors of 900
    • The prime factors of  900 = 2×2×3×3×5×5
  • Step 2: Square the similar factors n2
    • √900 = 22 ×32 ×52
  • Step 3: Multiply the squares
    • √900 = 2 ×3× 5

Hence, √900 = 30

Long division method

Find the number that can divide 900 equally with no reminder and use it as the dividend. Continue the process until zero is reached.

Long division method
Long division method

Hence, √900 = 30

Solved examples

Q1: The roots of – (900) and (900) are the same, what did you think?
A1: The negative square has no real root.
900 has real roots while  – (900) has only imaginary roots.
Hence, they are not similar

Q2: Robert wants to simply 900 to its simplest form, come let’s help her
A2: √900 = 2× 3× 5
Hence the simplest form of  √900 = 30

Q3: solve 2√900 + 1√900 
A3: The √900 = 30
= 2 (30) + 1 (30)
= 60 + 30
Hence, by solving 2√900+ 1√900= 90

Q4: what is the value of x, if x (900) = 30
A4: x (900) = 30
√900 = 30
Hence, x 30 = 30
X = 30/30 = 1
Therefore x = 1.

Q5: Find the perimeter of the square if the area of the square tile is 900.
A5: The area of the tile = √area = √900 = 30
The square tile has 4 sides therefore we multiply it by 4 = 4 ×30 = 120
Therefore the perimeter of the tile  = is 120 units.

Frequently asked questions

What is the square root of 900?
√900 = 2 ×3× 5
Hence, the square root of √900 = 30.

Explain why the square root of 900 is a rational number
When finding the prime factor of 900 we get 302 which is entirely an even power hence all the numbers are positive integers which makes them rational numbers.

What is the value of 900 and the square root of 900?
The square root of √900 is 30,
therefore 900×900 = 900 √30
Hence the value = 2700

What is the real value for the square root of 900
The square root of 900 is 30. When the square of the number gives the original value that is the square root of the number, or the inversion of the square root is just the squaring of the number. When the number 30 is squared we get 900.

What is the square root of 25?
The prime factor of 25 = 5×5
Hence, the square root of 25 = 5

What is the square root of (-900)?
The square root of minus digits is imaginary numbers or imaginary units which really don’t have a square root.
therefore the √-900 = 30i

Is 900 a perfect square number?
Yes, 900 is a perfect square number. because when the number is inversed by squaring the roots we exactly get the given number.

We hope that this article helped you in answering your queries regarding the square root of 900!

Written by

Prerit Jain

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