How to Estimate Square Roots

In this post, we are going to learn a new trick. This is on how to estimate square roots. Suppose that you forgot your calculator and you have to calculate square root. Although you have no calculator, you are familiar with may perfect squares. For example, 13^2 (thirdteen squared) is 169 and 8^2 = 64. Let’s see how we can use this stock knowledge on estimating square roots.

How to Estimate Square Roots

Example 1: How do we estimate the square root of 87?

Step 1: Get the nearest perfect square and get its square root. In this case, we have 81 which has a square root of 9.

Step 2: Divide the number by square root obtained in Step 1. So, we have 87/9 = 9.6667

Step 3: Average the result in Step 1 and Step 2. That is

(9 + 9.6667)/2 =9.3333

If you use your calculator, the square root of 87 is equal to 9.3273. 

Example 2: Estimate the square root of 125.

Step 1: Get the nearest perfect square and get its square root. In this case, we have 121 which has a square root of 11.

Step 2: Divide the number by square root obtained in Step 1. So, we have 125/11 = 11.3636

Step 3: Average the result in Step 1 and Step 2. That is

(11 +11.363636)/2 =11.1818

If you use your calculator, the square root of 125 is equal to 11.1803

That’s it for our trick today.  Subscribe to learn more tricks from Math Tricks For Kids.

 

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