#### Finding the Square Root of a Number

Finding the square root of a number involves determining what number, when multiplied by itself, equals the given number. Here are several methods to find the square root:

**By Hand (Long Division Method):**- This method involves long division and is suitable for finding square roots manually. It’s similar to the long division you may have learned for whole numbers.
- It’s a bit complex and time-consuming, so it’s not commonly used for large numbers or in everyday situations.

**Using a Calculator:**- Most scientific calculators and even basic calculators have a square root function. You can enter the number and press the square root button to find the square root directly.
- On smartphones or computers, you can also use the calculator app or search for “square root of [number]” in a search engine, and it will provide you with the result.

**Estimation:**- For rough estimates, you can use your knowledge of perfect squares to estimate the square root.
- For example, to find the square root of 36, you might know that 36 is a perfect square (6 x 6 = 36), so the square root of 36 is 6.

**Using Newton’s Method:**- Newton’s method is an iterative numerical method used to approximate the roots of a real-valued function. It can also be used to find square roots.
- This method involves repeatedly improving an approximation to the square root of a number until it’s accurate enough for your needs. It’s more complex and typically used in programming or advanced mathematics.

**Using the Prime Factorization Method:**- This method involves breaking down the number into its prime factors and then taking out pairs of the same prime factors.
- For example, to find the square root of 144, you can factor it as 2² × 3² × 2² = (2 × 3 × 2)² = 12² = 144, so the square root is 12.

For most practical purposes, using a calculator or estimation method is the quickest and easiest way to find the square root of a number. However, if you’re interested in the mathematical principles behind finding square roots, methods like long division or Newton’s method provide deeper insights.