Understanding the Square Root of 21

Result

√21 = 4.582576

Step-by-Step Process

Step 1: Find the Prime Factors of 21

The prime factors of 21 are: 3, 7

Properties of Square Root 21

  • Square: 21
  • Square Root: 4.582576
  • Number Type: Irrational
  • Perfect Square: No

Practical Applications

Geometry

If you have a square with an area of 21 square units, each side would measure √21 units.

Pythagorean Theorem

In a right triangle, if the hypotenuse measures 21 units, and one leg equals the other, each leg would measure √10.5 units.

Calculation Methods

Division Method

To approximate √21, you can use the division method:

  1. Take an approximate number (x)
  2. Divide 21 by x
  3. Average x with the result
  4. Repeat the process for greater accuracy

Frequently Asked Questions

What is the square root of 21?

The square root of 21 is 4.58257569495584, which is the number that, when multiplied by itself, gives 21.

Is 21 a prime number?

No, 21 is not a prime number.

Is √21 a rational or irrational number?

√21 is an irrational number because it cannot be expressed as an exact fraction of two integers.

How to simplify √21?

To simplify √21, we look for the largest perfect square that divides 21 and take it out of the root.