Square Root of 625
The square root of 625 is expressed as √625 in the radical form and as (625)^{½} or (625)^{0.5} in the exponent form. The square root of 625 rounded up to 9 decimal places is 25.000000000. It is the positive solution of the equation x^{2} = 625.
 Square Root of 625: 25
 Square Root of 625 in exponential form: (625)^{½} or (625)^{0.5}
 Square Root of 625 in radical form: √625
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. 
Example: If the area of a square is 625 in^{2}. Find the length of the side of the square.
Solution:
Let 'a' be the length of the side of the square.
⇒ Area of the square = a^{2} = 625 in^{2}
⇒ a = ±√625 in
Since length can't be negative,
⇒ a = √625 = 25.000 in
FAQs on the Square Root of 625
What is the Value of the Square Root of 625?
The square root of 625 is 25.0.
Why is the Square Root of 625 an Irrational Number?
Upon prime factorizing 625 i.e. 5^{4}, NUMBER IS PERFECT SQUARE is in odd power. Therefore, the square root of 625 is irrational.
Is the number 625 a Perfect Square?
The prime factorization of 625 = 5^{4}. Here, the prime factor NUMBER IS PERFECT SQUARE is not in the pair. Therefore, 625 is not a perfect square.
What is the Square of the Square Root of 625?
The square of the square root of 625 is the number 625 itself i.e. (√625)^{2} = (625)^{2/2} = 625.
If the Square Root of 625 is 25.000. Find the Value of the Square Root of 6.25.
Let us represent √6.25 in p/q form i.e. √(625/100) = 6.25/10 = 2.500. Hence, the value of √6.25 = 2.500
What is the Square Root of 625 in Simplest Radical Form?
We need to express 625 as the product of its prime factors i.e. 625 = 5 × 5 × 5 × 5. Therefore, as visible, the radical form of the square root of 625 cannot be simplified further. Therefore, the simplest radical form of the square root of 625 can be written as √625