Square Root of 900
Square root of a number is the value which on multiplication by itself, gives the original number. In this lesson, you will learn the square root of 900 and how to find square root of 900.
 Square Root of 900: 30
 Square of 900: 810000
What Is the Square Root of 900?
The square root of a number is a number whose square gives the original number. For example, to find the square root of 900 (which is denoted by √900), we have to think of a number that multiplies by itself to give 900. In short, a square root is a number which when squared gives the original number.
You can remember it this way: When the square moves from one side to the other side of the equation, it becomes the square root. 30^{2 }= 900 ⇒ √900 = 30. Thus, the square root of 900 is 30.
Is Square Root of 900 Rational or Irrational?
Important Notes
 If we do not have pairs of the same numbers as above, then the prime factorization cannot be used to find the exact square root. Instead, we have to use the long division method.
 The prime factorization method is used to write a square root of a nonperfect square number in the simplest radical form.
How to Find Square Root of 900?
We can find the square root of 900 using various methods.
 Repeated Subtraction
 Prime Factorization
 Estimation and Approximation
 Long Division
Should you wish to learn more about each of these methods, you may learn it here. Since we could find that 900 is a perfect square, we can find its square root using the prime factorization easily.
Square Root of 900 Using Prime Factorization
The prime factorization of 900 can be found as 2 × 2 × 3 × 3 × 5 × 5. To find the square root of 900, we take one number from each pair of the same numbers and we multiply them.
Hence, √900 =√(2 × 2 × 5 × 5 × 3 × 3) = 2 × 5 × 3 = 30
Square Root of 900 by Long Division
The square root of 900 can be found using the long division as follows:
Think of a number which when multiplied by itself gives a number that is less than or equal to 900 or a number that is very close to 900.
Since the remainder is 0, we do not need to proceed with long division further and we consider the quotient (which is 30) as the result.
Think Tank
 Can the value of √900 be 30 as well? Hint: Think what is (−30)^{2}.
 Is √−900 a real number? Think about whether there is any real number whose square is negative.
Explore Square roots using illustrations and interactive examples
Square Root of 900 Solved Examples

Example 1 John is instructed to find the square root of 900 using the laws of exponents. Can you help him with this?
Solution
The square root can be always replaced with the exponent 1/2.
√900= 900^{1/2 }= (30^{2})^{1/2 }[∵ 30^{2 }= 900] = 30
Thus, ∴ √900=30 
Example 2 Daniel is trying to figure out whether 900 and 2500 are perfect squares. What method can he use to find the square roots of 2500 and 900 quickly?
Solution
Daniel can figure out the square root of 2500 and the square root of 900 by various methods. By using the division method, he will get:
2500 ÷ 50 = 50
Therefore, 50 × 50 = 2500, and hence, 2500 is a perfect square with square root 50
Also,
900 ÷ 30=30
Therefore, 30 × 30 = 900, and hence, 900 is a perfect square with square root 30
FAQs on Square Root of 900
1. What is a square root of 900?
As we learned on this page, the square root of 900 can be either 30 or 30.
2. Is 900 a perfect square?
Yes, 900 is a perfect square. A perfect square is a number that can be expressed as the square of a number and 30 × 30 = 900.
3. What is the prime factorization of the square root of 900?
√900=√(2 × 2 × 5 × 5 × 3 × 3) = 2 × 5 × 3 = 30
4. Is the square root of 900 rational or irrational?
The square root of 900 is a rational number because it can be expressed in p/q form.