Square Root of 625

Square root of 625 is 25 and is represented as √625 = 25. 

A square root is an integer (can be either positive or negative) which when multiplied with itself, results in a positive integer called as the perfect square number. Here 625 is a perfect square because 625 can be obtained by multiplying either 25 by 25 (25 × 25) or it can also be obtained by multiplying -25 by -25 (-25 × -25). Therefore ± 25 is the square root of 625. 

The square root of any number can be obtained by using the prime factorisation method, long division method, simplified method and repeated subtraction method. 

Note the Following:

The Square root of 625 = √625 where √ = radical, and 625 is the radicand.

Exponential Form of Square root of 625 = 625^1/2

Solution for √625 = 25

Square root of 625 is Irrational = Fasle

For the detailed explanation on square roots can be obtained from What is Square root?

What is the Square root of 625?

The square root of 625 is 25. In other words, the square of 25 is 625. i.e ±25 × ±25 is 625. 

How to Find the Square root of 625?

There are three methods to find the Square root of 625:

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

Square root of 625 by Prime Factorisation Method

In the Prime Factorisation method, the following steps are followed;

1. Divide 625 by prime divisors. Only 5 divides 625.
2. Group same two prime number and remove 1 from the root
3. Product of the number outside the root forms the square root of 625.

Above steps for 625 will be expressed as;

625 = 5 × 5 × 5 × 5

625 = (5 × 5) × (5 × 5) 

√625 = √((5 × 5) × (5 × 5) 

√625 = 5 × 5

√625 = 25

Therefore the square root of 625 = 25.

Square root of 625 by Long Division Method

In the long division method, the given numbers are paired in groups, starting from the right side. Let us understand the long division method, in detailed steps;

Step 1:  Grouping the given number into pairs

Given number is 625, grouping it as 2 and 56.

Step 2: Consider the first number.

Let us find a square number that divides the first number

i.e., 

1 × 1 = 1 

2 × 2 = 4 

3 × 3 = 9.

Step 3: Continue the division using the next number 25. The first number to be used as the next divisor (Divisor of first division multiplied by quotient of first division)

Since the Division is complete with remainder as zero, the quotient becomes the square root of the given number. 

Therefore the Square root of 625 is 25.

Square root of 625 by Repeated Subtraction Method.

In the repeated subtraction method, the number 625 is subtracted repeatedly by odd numbers. There are two possibilities

1. Difference becomes zero after repeated subtraction: Then the number 625 is a perfect square and the step number is the square root of 625.
2. Difference becomes negative after repeated subtraction: Then the number 625 is not a perfect square and it does not have a rational root. 

For the given number 625, steps for repeated subtraction are

Step 25 leads to the difference zero, which implies that 625 is a perfect square number and hence 25 is its root. 

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Solved Examples

1. Find the square root of 625 by pairing factors.

The pairs of 625 are (1, 625), (5, 125) and (25, 25)

Therefore the square root of 625 is 25 using pairing factors 25 and 25. 

2. What is the square of 25?

The square of 25 is nothing but 25 times 25 and that is 625.