How to find square root approximation?

Finding an approximate square root can be done using a simple technique involving a known square and a small adjustment. This method provides a quick way to estimate square roots without a calculator.

Approximation Technique

The core idea is to find a perfect square close to the number you want to find the square root of. Then, you adjust this known square root to get a closer approximation. According to the TalentSprint video, the method can be summarized as follows:

1. Identify a nearby perfect square: Find a perfect square (A²) that is close to the given number (N) for which you want to find the square root.

2. Calculate the difference: Determine the difference between the given number (N) and the perfect square (A²). This is (N - A²).

3. Divide by 2A: Divide the difference by 2 times the square root of the perfect square (2 * A).

4. Add to the known square root: Add the result from step 3 to the square root of the perfect square (A). This gives you the approximate square root of N.

   Therefore, the approximate square root of N is: A + (N - A²) / (2 * A)

Example

Let's say we want to approximate the square root of 38.

• The nearest perfect square is 36 (6²). So, A = 6.
• The difference between 38 and 36 is 2 (N - A² = 38 - 36 = 2).
• Divide the difference by 2 * A: 2 / (2 * 6) = 2 / 12 = 1/6 = 0.1667
• Add this to A: 6 + 0.1667 = 6.1667

Therefore, the approximate square root of 38 is 6.1667. (The actual square root of 38 is approximately 6.1644, so this is a very close approximation).