Square Root of 1025

The square root of 1025 is irrational. The approximate value of the square root of 1025 is 32.02. If an integer “r” is multiplied with the same “r” then the product is termed as the perfect square number, say “p”. Representing this definition with Mathematical notation will be “r × r = p”, where r = integer/square root and p = integer/perfect square number. Squares and square roots are used in finding the area of a circle, Pythagorean theorem and its applications. There are three common ways of calculating the square root of any given number. They are by prime factorisation method, long division method or repeated subtraction method, which are all detailed below. More on squares and their roots can be found at Squares and Square roots.

Note the Following:

• The Square root of 1025 = 2√1025 = √1025 where ‘√’ is the radical, and 1025 is the radicand and 2 is the index.
• Exponential Form of Square root of 1025 = 1025^1/2
• Solution for √1025 = 5 √41 ≈ 32.02
• The square root of 1025 is Irrational = True

What is the Square root of 1025?

The square root of 1025 is 32.01, as the square root of 1025 is irrational.

How to Find the Square root of 1025?

There are three methods to find the Square root of 1025 

• Prime Factorisation method
• Long Division method
• Repeated Subtraction method

Square root of 1025 by Prime Factorisation Method

In the prime factorization method, the following steps are performed;

1. Divide 1025 by prime factors, starting from 5.
2. Group the two same prime factors and remove them from square root ( √)
3. Only 1 prime factor from a group of 2 should be considered outside of the square root (√)

Let us apply the above steps for 1025.

The prime factors are 5, 5 and 41. Since this is a square root, two 5’s can be removed from within the root, as 5. i,e √1025 = √(5× 5 × 41) = 5√41. 

Square root of 1025 by Long Division Method

To understand the long division method, follow the below mentioned detailed steps;

Step 1: Group the given number into pairs. 

Step 2: Divide the first pair, using the divisor such that the product is less than or equal to.

Step 3: Continue the division, by bringing the next pair.

Step 4: The first divisor in the next division to be  (Divisor of first division + quotient of first division) such that:

d1 × 1 =

d2 × 2 =

d3 x 3 =

 And so on. 

Step 5: If the division is complete with the remainder as zero, then the quotient will be the square root. Else the number is not a perfect square number.

Applying the above steps to 1025.

Pairing 10 and 25.

The squares are: 

1 × 1 = 1

2 × 2 = 4

3 × 3 = 9

This implies that 1025 does not have a perfect square root. 

Hence 1025 is irrational and the root lies between 32 and 33.

Square root of 1025 by Repeated Subtraction Method.

In the repeated subtraction method, the number 1025 is subtracted successively by the odd numbers starting with 1. If, at any point, the difference is zero, then the number 1025 is a perfect square. If the difference at any point becomes negative, then 1025 is not a perfect square number and the root lies between the step where the difference changed from positive to negative. 

Let us observe the repeated subtraction steps from the table below for 1025.

The difference changes from positive to negative from step 32 to step 33. Hence 1025 has an irrational root that lies between 32 and 33.

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Solved Examples

1. Does 1025 have a perfect square root?

Solution: No. 1025 does not have a perfect square root.

2. What is the square of 1025?

Solution: 1025 square is 1050625.