Understanding the Square Root of 17

Result

√17 = 4.123106

Step-by-Step Process

Step 1: Find the Prime Factors of 17

17 is a prime number.

Since 17 is a prime number, the square root of 17 is already in its simplest form.

Properties of Square Root 17

  • Square: 17
  • Square Root: 4.123106
  • Number Type: Irrational
  • Perfect Square: No

Practical Applications

Geometry

If you have a square with an area of 17 square units, each side would measure √17 units.

Pythagorean Theorem

In a right triangle, if the hypotenuse measures 17 units, and one leg equals the other, each leg would measure √8.5 units.

Calculation Methods

Division Method

To approximate √17, you can use the division method:

  1. Take an approximate number (x)
  2. Divide 17 by x
  3. Average x with the result
  4. Repeat the process for greater accuracy

Frequently Asked Questions

What is the square root of 17?

The square root of 17 is 4.123105625617661, which is the number that, when multiplied by itself, gives 17.

Is 17 a prime number?

Yes, 17 is a prime number.

Is √17 a rational or irrational number?

√17 is an irrational number because it cannot be expressed as an exact fraction of two integers.

How to simplify √17?

Since 17 is a prime number, √17 is already in its simplest form.