Understanding the Square Root of 117

Result

√117 = 10.816654

Step-by-Step Process

Step 1: Find the Prime Factors of 117

The prime factors of 117 are: 3, 3, 13

Properties of Square Root 117

  • Square: 117
  • Square Root: 10.816654
  • Number Type: Irrational
  • Perfect Square: No

Practical Applications

Geometry

If you have a square with an area of 117 square units, each side would measure √117 units.

Pythagorean Theorem

In a right triangle, if the hypotenuse measures 117 units, and one leg equals the other, each leg would measure √58.5 units.

Calculation Methods

Division Method

To approximate √117, you can use the division method:

  1. Take an approximate number (x)
  2. Divide 117 by x
  3. Average x with the result
  4. Repeat the process for greater accuracy

Frequently Asked Questions

What is the square root of 117?

The square root of 117 is 10.816653826391969, which is the number that, when multiplied by itself, gives 117.

Is 117 a prime number?

No, 117 is not a prime number.

Is √117 a rational or irrational number?

√117 is an irrational number because it cannot be expressed as an exact fraction of two integers.

How to simplify √117?

To simplify √117, we look for the largest perfect square that divides 117 and take it out of the root.