Square Root of 9025

The square root is the inverse of the square of the number. 9025 is a perfect square. The square root of 9025 is expressed in both radical and exponential form. In the radical form, it is expressed as √9025, whereas (9025)^(1/2) in the exponential form. √9025 = 95, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

The prime factorization method and the long division method can be used to find the square root of perfect square numbers like 9025. Let us now learn the following methods:

• Prime factorization method
• Long division method

The product of prime factors is the prime factorization of a number. Now let us look at how 9025 is broken down into its prime factors.

Step 1: Finding the prime factors of 9025

Breaking it down, we get 5 x 5 x 19 x 19: 5^2 x 19^2

Now we found out the prime factors of 9025. The second step is to make pairs of those prime factors. Since 9025 is a perfect square, we can pair the factors (5 x 19) and take one factor from each pair to find the square root.

The long division method is another way to find the square root of perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step:

Step 1: To begin with, we need to group the numbers from right to left into pairs. In the case of 9025, we group it as 90 and 25.

Step 2: Now we need to find a number whose square is less than or equal to 90. We can choose 9 because 9 x 9 = 81, which is less than 90. Now the quotient is 9, and after subtracting 81 from 90, the remainder is 9.

Step 3: Bring down the next pair, 25, to make the new dividend 925. Add the old divisor 9 to itself (9 + 9 = 18), which becomes our new divisor.

Step 4: Find n such that 18n x n ≤ 925. Considering n as 5, (180 + 5) x 5 = 925.

Step 5: Subtract 925 from 925, and the remainder is 0.

So the square root of √9025 is 95.

Approximation method is another method for finding the square roots, but since 9025 is a perfect square, we have already found its square root exactly.

Step 1: We identify the closest perfect square of √9025, which is 9025 itself. Since 9025 is already a perfect square, the approximation is not needed, and √9025 = 95.

• Square root: A square root is the inverse of a square. Example: 9^2 = 81, and the inverse of the square is the square root, that is, √81 = 9.
   
• Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.
   
• Perfect square: A perfect square is a number that is the square of an integer. For example: 9025 is a perfect square because it is 95^2.
   
• Prime factorization: The expression of a number as a product of prime numbers. For example, the prime factorization of 9025 is 5^2 x 19^2.
   
• Divisor: A divisor is a number that divides another number completely without leaving a remainder. For example, 5 is a divisor of 9025.