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.

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.
 

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.
 

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.
 

• 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