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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 is 25. It is the positive solution of the equation x2 = 625. The number 625 is a perfect square.

  • 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
  • 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.
  • The square root of 625, 25 can be expressed in the form of p/q, that is 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: 54
  • 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 below-given steps we will find the square root of 625 by the long division method.

  • Refer to the below-given 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.

Square root of 625

We get a square root of √625 = 25 by the long division method.

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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

  1. 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= (54)1/4
    So, (625)1/4= ±5 or √√625 = ±5.

  2. 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 = 54
    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.

  3. Example 3: If the area of a square is 625 in2. 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 = a2 = 625 in2
    ⇒ a = ±√625 in
    Since length can't be negative,
    ⇒ a = √625 = 25 in

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FAQs on the Square Root of 625

What is the Value of the Square Root of 625?

The square root of 625 is 25.

Why is the Square Root of 625 a Rational Number?

Upon prime factorizing 625 i.e. 54, we find that all the prime factors are in even power. This implies that the square root of 625 is a positive integer. Therefore, the square root of 625 is rational.

Evaluate 20 plus 9 square root 625

The given expression is 20 + 9 √625. We know that the square root of 625 is 25. Therefore, 20 + 9 √625 = 20 + 9 × 25 = 20 + 225 = 245

What is the Square Root of -625?

The square root of -625 is an imaginary number. It can be written as √-625 = √-1 × √625 = i √625 = 25i
where i = √-1 and it is called the imaginary unit.

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. Find the Value of the Square Root of 6.25.

Let us represent √6.25 in p/q form i.e. √(625/100) = 25/10 = 2.5. Hence, the value of √6.25 = 2.5

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