how do i estimate a square root of a number thats not a perfect square? Without using a calculator. Also, what are square roots?

Im really confused

Square root is a number, when multiplied by itself, gives your that number, e.g.,

2*2 = 4, 3*3 = 9.

Find the square roots of the numbers on either side of the number to estimate the square root of the number,e.g., √6 = approximately 2.5. Also there are tables to give you square roots, so √6 = 2.4495. You can probably find square roots on a calculator or iPhone.

To estimate the square root of a number that is not a perfect square, you can use a method called the "approximation method." Here's how you can do it:

1. Start by finding the two perfect squares between which your number falls. For example, if you want to find the square root of 12, the perfect squares near it are 9 (3^2) and 16 (4^2).

2. Take the lower perfect square (in this case, 9) and divide your number (12) by it. The result will be your initial estimate: 12 ÷ 9 = 1.33.

3. Now, refine your estimate. You can do this step by step, improving your estimate each time based on how close it is to the actual square root. In this case, take the average of your estimate and the divisor. The average of 1.33 and 9 is approximately 5.17.

4. Repeat the process by dividing your original number (12) by this refined estimate (5.17), which gives you a new estimate: 12 ÷ 5.17 = 2.32.

5. Continue this iterative process until your estimate becomes stable and does not change significantly. The more iterations you do, the more accurate your estimate will become.

Square roots represent the number that, when multiplied by itself, equals a given number. For example, the square root of 9 is 3 because 3 × 3 = 9. In other words, it is the "opposite" of squaring a number. Square roots are denoted by the symbol (√) and can be either positive or negative, as both positive and negative numbers squared give the same result.