# Hello World Square Roots 1 2 3 Strategies

Solving square roots using hello world square roots 1 2 3 strategies is both fun and challenging. The square root is often considered the trickiest basic mathematical operations to solve. Finding the square of any number is easy because you are multiplying a number by itself to discover one result. There are two numbers involved in the calculation (although both numbers are the same) and only one number to discover. In a square root operation, you only have one number to calculate to discover its square root. With the 3-step strategy—hence 1 2 3—that will be explained below, you can figure out the square root of a number, be it an integer or non-integer, quite easily.

The calculation strategy will be divided into two parts. The first part, which includes 2-step strategy, helps you reveal the integer square root of a number and the second part, which is a 1-step strategy, helps you reveal the non-integer square root of a number.

How to Find the Integer Square Root of a Number

A number may have an integer or non-integer square root. 1, 4, and 9 are examples of numbers that have integer square roots (1, 2, and 3 respectively). Finding the square root of any number from 1 to 100 is fairly easy because there are only 10 square roots that are easy to memorize. What if you have to find the square root of a number bigger than 100? There are two easy steps that you can take.

• Check the last digit.

Suppose you are going to find the square roots of 841 and 3844. The first of the hello world square roots 1 2 3 strategies that you should do is checking the last digit, which is 1 and 4 respectively.

You should understand that the last digit of a number can be associated with the square of any numbers from 1 to 10. The square of 1 and 9 ends with 1, the square of 2 and 8 ends with 4, the square of 3 and 7 ends with 9, the square of 4 and 6 ends with 6, the square of 5 ends with 5, and the square of 10 ends with 0.

By checking the last digit, you should be able to guess that the square root of 841 must be a number that ends with 1 or 9 and the square root of 3844 must be a number that ends with 2 or 8.

• Check the first digit.

After you check the last digit, you should check the first digit or digits to the unit of hundreds. Therefore, for 841 the number that you should check is 8 and for 3844 it is 38. Look for any square numbers nearest the referenced number.

For 8, 4 should be the nearest square number and for 38, it is 36. The square root of each number respectively is 2 and 6. From this calculation, you can guess that the square root of 841 is either 21 or 29 and the square root of 3844 is either 62 or 68. With a simple multiplication operation, you can easily conclude that 29 is the square root of 841 and 62 is the square root of 3844.

How to Find the Non-Integer Square Root of a Number

The third step is specifically useful for discovering the non-integer square root of a number. As you already know, not all numbers have integer square roots. In fact, most of them have non-integer square root that is rather hard to find.

However, with the third step of the 1 2 3 strategies, you can easily find the non-integer square root of any number with quite a simple calculation. The key of this step is to divide the number by a set of numbers that have integer square roots.

Suppose you are going to find the square root of 108. This number has factors that include numbers with integer square roots, i.e. 4, 9, and 36. Let’s pick the biggest number, 36. With a simple calculation, you can deduce that 108 = 36 x 3, so √108 = √36 x √3. With a simple step of hello world square roots 1 2 3 strategies, you can conclude that the square root of 108 is 6√3.