Square root of 625
The square root of 625 is also a perfect square (25). The number 625 is a special number with 5 as the only factor. The square root of a number is a number whose product with itself gives the given number. Now we will see different methods to calculate the square root of 625 along with some interesting questions.
 Square root of 625: √625 = 25
 Square of 625: 625^{2} = 390625
1.  What Is the Square Root of 625? 
2.  Is Square Root of 625 Rational or Irrational? 
3.  How to Find the Square Root of 625? 
4.  FAQs on Square Root of 625 
What is The Square Root of 625?
 Square root of 625 is written as √625 (Radical form).
 Square root of 625 = √625 = √(25 × 25) = +25 and 25.
 In the exponential form, the square root of 625 is expressed as (625)^{1/2}.
Is Square Root of 625 Rational or Irrational?
 If a number can be represented in the form of p/q where q ≠ 0, then the number is a known rational number.
 Both the square of 625, +25, and 25 can be expressed in the form of p/q, that is +25/1 and 25/1.
 Hence, the square root of 625 is a rational number.
How to Find the Square Root of 625?
We will now calculate the square root of 625 by prime factorization or long division method.
Square Root of 625 By Prime Factorization Method
 Step 1: Prime factorization of 625: 5^{4}
 Step 2: Prime factors of 625 in pairs: (5 × 5) × (5 × 5)
 Step 3: Now square root of 625:
√625 = √(5 × 5) × (5 × 5)
√625 = √(5 × 5)^{2}
√625 = √(25)^{2} = ±25
Therefore, the square root of 625 is ±25.
Square Root of 625 By Long Division
Now by following the belowgiven steps we will find the square root of 625 by the long division method.
 Refer to the belowgiven figure and pair the digits from the right end in pairs of two by putting a bar on top of them. So, we get two pairs of 6 and 25.
 Now we need to find a number (n) such that n × n is a number less than equal to 6. So, we get n = 2. As 2 × 2 = 4 (Which is less than 6).
 Now subtract 4 from the first pair (6) in the dividend we get 2 as remainder.
 Now add the divisor with itself (2+2) and bring the second pair down (25).
 Now find a number at the unit’s place (m) such that 4m × m is less than equal to 225. Here m will be 5 as 45 × 5 = 225.
We get a square root of √625 = 25 by the long division method.
Explore square roots using illustrations and interactive examples
Important Notes:
 625 is a perfect square.
 The square roots of 625 are integers.
 The square root of 625 is also a perfect square, that is +25.
Square Root of 625 Solved Examples

Example 1: Jason needs to find the value of √√625. Can you help Jason?
Solution:
We know that √√625 can also be written as ((625)^{1/2})^{1/2 }which can be further simplified to (625)^{1/4}.
As (625)^{1/4} = (5 × 5 × 5 × 5)^{1/4}
(625)^{1/4}= (5^{4})^{1/4}
So, (625)^{1/4}= ±5 or √√625 = ±5. 
Example 2: Find the smallest multiple of 625 that will be a perfect square?
Solution:
Multiples of 625 = 625, 1250, 1875, 2500, 2125, 2750……...
Prime Factorization of 625 = 5^{4}
If we multiply it by the smallest perfect square we will get the required multiple. Therefore, multiplying 625 × 4 = 2500. Hence, 2500 is the smallest multiple of 625 which is a perfect square.
FAQs on Square Roots of 625
Write the prime factors of 625 and the prime factorization of 625.
 Prime factor of 625 is 5.
 Prime factorization of 625 is 5^{4}.
By what number 625 should be divided to make it a perfect cube?
A perfect cube is a number whose factors are the cube of a number. To make 625 perfect a cube, we have to divide them by 5.
Can we find the square root of 625 by the repeated subtraction method?
Yes, we can find the square root of 625 using the repeated subtraction method. Because 625 is a perfect square so we can use this method.
What is the square root of 625?
The square root of negative numbers are imaginary numbers. Square root of 625 are, √625 = ±25i.
Are the square roots of 625 rational?
The square roots of 625 are, ±25. Both +25 and 25 can be expressed in the form of p/q. So, the roots of 625 are rational.