Understanding the Square Root of 120

Result

√120 = 10.954451

Step-by-Step Process

Step 1: Find the Prime Factors of 120

The prime factors of 120 are: 2, 2, 2, 3, 5

Properties of Square Root 120

  • Square: 120
  • Square Root: 10.954451
  • Number Type: Irrational
  • Perfect Square: No

Practical Applications

Geometry

If you have a square with an area of 120 square units, each side would measure √120 units.

Pythagorean Theorem

In a right triangle, if the hypotenuse measures 120 units, and one leg equals the other, each leg would measure √60.0 units.

Calculation Methods

Division Method

To approximate √120, you can use the division method:

  1. Take an approximate number (x)
  2. Divide 120 by x
  3. Average x with the result
  4. Repeat the process for greater accuracy

Frequently Asked Questions

What is the square root of 120?

The square root of 120 is 10.954451150103322, which is the number that, when multiplied by itself, gives 120.

Is 120 a prime number?

No, 120 is not a prime number.

Is √120 a rational or irrational number?

√120 is an irrational number because it cannot be expressed as an exact fraction of two integers.

How to simplify √120?

To simplify √120, we look for the largest perfect square that divides 120 and take it out of the root.