Understanding the Square Root of 46

Result

√46 = 6.782330

Step-by-Step Process

Step 1: Find the Prime Factors of 46

The prime factors of 46 are: 2, 23

Properties of Square Root 46

  • Square: 46
  • Square Root: 6.782330
  • Number Type: Irrational
  • Perfect Square: No

Practical Applications

Geometry

If you have a square with an area of 46 square units, each side would measure √46 units.

Pythagorean Theorem

In a right triangle, if the hypotenuse measures 46 units, and one leg equals the other, each leg would measure √23.0 units.

Calculation Methods

Division Method

To approximate √46, you can use the division method:

  1. Take an approximate number (x)
  2. Divide 46 by x
  3. Average x with the result
  4. Repeat the process for greater accuracy

Frequently Asked Questions

What is the square root of 46?

The square root of 46 is 6.782329983125268, which is the number that, when multiplied by itself, gives 46.

Is 46 a prime number?

No, 46 is not a prime number.

Is √46 a rational or irrational number?

√46 is an irrational number because it cannot be expressed as an exact fraction of two integers.

How to simplify √46?

To simplify √46, we look for the largest perfect square that divides 46 and take it out of the root.