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Kiến Thức Y Khoa 25/08/2023

184 3 minutes read

Have you ever wondered how to quickly calculate the square of a number? Multiplying a number by itself is the simplest way, but when dealing with two-digit numbers like 45 or 89, mentally calculating their squares can be time-consuming. That’s why we’re here to help you learn the fastest ways to calculate squares.

Table of Contents

What is a Square?

A square (also known as a power of two) is the product of a number multiplied by itself.

Symbol: x.x = x²
The number x is referred to as the base.
It can be read as “the square of x,” “x squared,” or “x to the power of two.”

For example:

52 can be read as the square of 5, 5 squared, or 5 to the power of two.
62 is the square of 6, 6 squared, or 6 to the power of two, which is 62.

Fast Methods to Calculate Squares for Two-Digit Numbers with a Units Digit of 5

For two-digit numbers with a units digit of 5, we can use the following quick method to calculate their squares:

Step 1: Multiply the units digit (5) by itself to get the result of 25.
Step 2: Multiply the tens digit by the next consecutive number. For example, for the number 25, the tens digit is 2, and we multiply it by the next number (3) to get 2 * 3 = 6.
Step 3: Arrange the results from Steps 1 and 2 in the order of Step 2 followed by Step 1. The result is the square of the original number.

For instance, let’s calculate the square of the number 25:

Step 1: 5 x 5 = 25
Step 2: 2 x 3 = 6 (next consecutive number after 2 is 3)
Step 3: Arrange the results from Steps 2 and 3 in order: 1849

So, the square of 25 is 1849.

You can use this method for other numbers with a units digit of 5, such as 15, 35, 45, 65, 75, and 95.

Quick Methods to Calculate Squares for Two-Digit Numbers from 11 to 99

Method 1: Comparing with the Digits 50 and 25

This method involves the following steps:

For numbers smaller than 50 (e.g., 43):

Step 1: Subtract 25 from the number to be squared. For example, 43 – 25 = 18.
Step 2: Since 43 is less than 50, subtract it from 50 to get 50 – 43 = 7.
Step 3: Square the result from Step 2, which is 7² = 49.
Step 4: Arrange the numbers in order from left to right, following the sequence of Step 1, Step 3. In our example, the result is 1849.

For numbers greater than 50 (e.g., 53):

Step 1: Subtract 25 from the number. For example, 53 – 25 = 28.
Step 2: Since 53 is greater than 50, subtract 50 from it: 53 – 50 = 3.
Step 3: Square the number from Step 2, which is 3² = 9.
Step 4: Arrange the numbers from Step 1 and Step 3 in order, from left to right. If the result from Step 3 has only one digit, add a zero before it. For example, for 53, the result is 2809.

Method 2: Using the Tens and Units Digits

Except for numbers with a units digit of 5, you can apply the following method to quickly calculate the square of a two-digit number:

Let’s take 31 as an example:

Step 1: Add the number to be squared to its units digit. For instance, 31 + 1 = 32.
Step 2: Multiply the result from Step 1 by the tens digit of the original number. In this case, 32 x 3 = 96.
Step 3: Square the units digit, which is 2² = 4.
Step 4: Add a zero to the result from Step 2 and then add it to the result from Step 3. The final result is 961 for 312.

You can also watch the video tutorial on how to calculate squares quickly.

So, these are the quick methods you can use to calculate the square of two-digit numbers, making your calculations faster and easier.

Additional information: Learn how to simplify fractions quickly.