Understanding the Square Root of 48

Result

√48 = 6.928203

Step-by-Step Process

Step 1: Find the Prime Factors of 48

The prime factors of 48 are: 2, 2, 2, 2, 3

Properties of Square Root 48

  • Square: 48
  • Square Root: 6.928203
  • Number Type: Irrational
  • Perfect Square: No

Practical Applications

Geometry

If you have a square with an area of 48 square units, each side would measure √48 units.

Pythagorean Theorem

In a right triangle, if the hypotenuse measures 48 units, and one leg equals the other, each leg would measure √24.0 units.

Calculation Methods

Division Method

To approximate √48, you can use the division method:

  1. Take an approximate number (x)
  2. Divide 48 by x
  3. Average x with the result
  4. Repeat the process for greater accuracy

Frequently Asked Questions

What is the square root of 48?

The square root of 48 is 6.928203230275509, which is the number that, when multiplied by itself, gives 48.

Is 48 a prime number?

No, 48 is not a prime number.

Is √48 a rational or irrational number?

√48 is an irrational number because it cannot be expressed as an exact fraction of two integers.

How to simplify √48?

To simplify √48, we look for the largest perfect square that divides 48 and take it out of the root.