Square root of 900
2026-02-28 18:04 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-900

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Last updated on October 23, 2025

When someone asks you to explain a square root, you can just tell that it is a number when multiplied by itself produces the same number. As we continue with our explanation, let’s assume the value of 900 Here 900 is considered as a non-perfect square root since it contain either decimal or fraction. Let's learn more about square roots in this article.

What is the square root of 900?

The square root of 900 can be easily found out by using long division method. In which it is discovered that the cumulative approximation of √900 is 9.165.

Finding the square root of 900.

There are many ways through which students can find square roots, and some of these methods are very popular. Some of the methods have been explained in detail below.
 

Square root of 900 using the prime factorization method.

In this method, we decompose the number into its prime factors.


Prime factorization of 900: 900=22×32×52.


Since not all prime factors can be paired, 900 cannot be simplified into a perfect square. Therefore, the square root of 900 cannot be expressed in a simple radical form.
 

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Square root of 900 using the division method.

For non-perfect squares, we often use the nearest perfect square to estimate the square root. Follow these steps:


Step 1: Write the number 900 to perform long division.


Step 2: Identify a perfect square number that is less than or equal to 900. For 900, that number is 900 (302)(30^2)(302).


Step 3: Divide 900 by 30. The remainder will be 0, and the quotient will be 30.


Step 4: Since the remainder is 0, you can stop here; the square root is exact.


Step 5: In this case, you do not need to double the quotient or perform further calculations.
 

Common mistakes when finding the square root of 84.

Here are some common mistakes students should avoid while learning to calculate the square root of 84.

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Problem 1

Simplify 4√20 + 4√20.

Okay, lets begin

→ Factor √20


4√20 + 4√20


= √20(4+4) 


= 8×4.472


= 35.776
 

Explanation

Simplification of √20= 4.472, now if you add the 4 and 4 and multiply it by 4.472 we get 35.776.

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Problem 2

Simplify √12 × √36.

Okay, lets begin

√12 × √36


= √432
 

Explanation

 Here, we multiply 12 by 36 to get 432, which results in √432. Since 432 is not a perfect square, the result cannot be simplified further.

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Problem 3

Find the square root of 49.

Okay, lets begin

√49= 7
 

Explanation

The square root of 49 is going to be 7 as 7 multiplied by itself leads to 49.
 

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FAQs on the square root of 900.

1.What is the difference between square root and cube root.

 A square root of a number is a value that, when multiplied by itself, gives that number. The cube root is a value that, when multiplied thrice, the result is the said number.

2.3 is the square root of what number?

To find out what number 3 is the square root of, we need to multiply the number 3 with itself, the resulting number would be the answer in this case 3 × 3 is equal to 9

3.What is the prime factorization of 900?

Using the prime factorization method we can easily find out that 900 can be written as multiples of 2, 3, and 5 to be more specific 900 = 22 × 32 × 52.
 

4. How do you simplify 4√72?

 4√72 can be easily simplified to 24√2, as we can express √72 as 6√2. 4 × 6 is equal to 24 hence it will be written as 24√2.
 

5. Is 900 a perfect square?

Yes, 900 is indeed a perfect square number because the number 30 can be squared to get 900 (30 × 30=900). Perfect squares are nothing but squares of a whole number.

Important Glossaries for Square Root of 900

  • Square Root: A number which when multiplied by itself gives the original number is called a square root.
  • Perfect Square: A number that is the integral square of an integer I such that n = I², example I = 1, 2, 3, n = 1, 4, 9, 16, etc.
  • Prime Factorization: The ability to factorise a number into the product of the basic arithmetic numbers, also known as primary numbers.
  • Non-Perfect Square: A figure that cannot be converted into an integer figure once divided by itself (e.g., 76).
  • Approximation Method: Approximating square root, that is, finding the closest integer which, when squared, yields the number being approximated

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.