Is 125 a perfect square?

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 5√5
• 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.

\sqrt{125} = 11.1803398875

• The simplified radical form of the square root of 125 is:

\sqrt{125} = 5\sqrt{5}

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 ( \frac{p}{q} ), where both ( p ) and ( q ) are integers, and ( q \neq 0 ).
• The square root of 125 is ( \sqrt{125} \approx 11.1803398875 ), which cannot be expressed as an exact fraction of two integers.
• The simplified radical form is ( 5\sqrt{5} ), and since \sqrt{5} is irrational, 5\sqrt{5} 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:

125 = 5 \times 5 \times 5

Step 2: Group the identical pairs of prime factors:

125 = (5 \times 5) \times 5

Step 3: Take the square root:

\sqrt{125} = \sqrt{(5 \times 5) \times 5} = 5\sqrt{5}

The simplified radical form of ( \sqrt{125} ) is ( 5\sqrt{5} ).

2. Decimal Approximation Method:

If you need the approximate decimal value:

\sqrt{125} \approx 11.1803398875

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 ( 5\sqrt{5} ) 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 ( n = m^2 ), where ( m ) is an integer, then ( n ) is a perfect square.
• For 125, there is no integer ( m ) such that ( m^2 = 125 ).
• The square root of 125 is ( \sqrt{125} = 5\sqrt{5} ), which is not an integer.
• Therefore, 125 is not a perfect square.