Understanding the Square Root of 137

Result

√137 = 11.704700

Step-by-Step Process

Step 1: Find the Prime Factors of 137

137 is a prime number.

Since 137 is a prime number, the square root of 137 is already in its simplest form.

Properties of Square Root 137

  • Square: 137
  • Square Root: 11.704700
  • Number Type: Irrational
  • Perfect Square: No

Practical Applications

Geometry

If you have a square with an area of 137 square units, each side would measure √137 units.

Pythagorean Theorem

In a right triangle, if the hypotenuse measures 137 units, and one leg equals the other, each leg would measure √68.5 units.

Calculation Methods

Division Method

To approximate √137, you can use the division method:

  1. Take an approximate number (x)
  2. Divide 137 by x
  3. Average x with the result
  4. Repeat the process for greater accuracy

Frequently Asked Questions

What is the square root of 137?

The square root of 137 is 11.704699910719626, which is the number that, when multiplied by itself, gives 137.

Is 137 a prime number?

Yes, 137 is a prime number.

Is √137 a rational or irrational number?

√137 is an irrational number because it cannot be expressed as an exact fraction of two integers.

How to simplify √137?

Since 137 is a prime number, √137 is already in its simplest form.