No, 125 is not a perfect square.
125 can be written as the sum of two squares in two distinct ways: 125 = 102 + 52 or 112 + 22. The square root of 125 is represented as 5 √5.
- Square Root of 125 is
- Square of 125 is 15,625
What Is the Square Root of 125?
- The square root is an inverse mathematical operation of a square.
- The square root of 125 is the value that is obtained after taking the square root of 125.
- The simplified radical form of the square root of 125 is:
Is the Square Root of 125 Rational or Irrational?
The square root of 125 is irrational .
Explanation:
- A number is considered rational if it can be expressed as a fraction , where both ( p ) and ( q ) are integers, and
- The square root of 125 is which cannot be expressed as an exact fraction of two integers.
- The simplified radical form is , and since is irrational, is also irrational.
- Therefore, the square root of 125 is an irrational number.
How to Find the Square Root of 125?
To find the square root of 125, you can follow these steps:
1. Prime Factorization Method:
Step 1: Find the prime factorization of 125:
Step 2: Group the identical pairs of prime factors:
Step 3: Take the square root:
The simplified radical form of
2. Decimal Approximation Method:
If you need the approximate decimal value:
This value is found using a calculator or by estimating the square root.
3. Understanding the Result:
The exact form is ( 5\sqrt{5} ).
The approximate decimal value is 11.18 (rounded to 2 decimal places).
The square root of 125 can be expressed as or approximately 11.18.
No, 125 is not a perfect square.
Conclusion:
- A perfect square is a number that can be expressed as the square of an integer. In other words, if , where ( m ) is an integer, then ( n ) is a perfect square.
- For 125, there is no integer ( m ) such that .
- The square root of 125 is , which is not an integer.
- Therefore, 125 is not a perfect square.
