Square of 72

In square numbers, the last digit of a square integer x will always be 0, 1, 4, 5, 6, or 9, if x is a positive integer. There is a possibility that children might get confused between ‘squaring’ a number and the ‘square root’ of a number. The square of 72 is the number that you multiply by itself twice (two times using the multiplication method), you get the square of that number. By ‘square number’, it means you are squaring the given number x raised to the power of 2, i.e., x² = x * x. 

Whereas, the ‘square root’ of a number is finding its root number that when multiplied by itself gives the original number. That is, x = y, where y is the square root of x. Always remember that square numbers and square roots give opposite actions and not the same results. 

In the case of the square 72, the number 72 is multiplied by itself twice to give 5184. And the square root of 5184 is ±72 (see the opposite actions here). The square of 72 can be written in exponential form as 72². It can also be written in an arithmetic form as 72 x 72. 

To calculate the square of a number, just multiply the number by itself using ‘’ (multiplication sign). That is, to multiply the given number by itself again. To find the square of 72, we use the following three methods.

• By Multiplication Method
• Using a Formula (a²)
• Using a Calculator

Using this method, each digit of one number is multiplied by the digits of the other number, and the results are then altogether added. Here is the gradual one-by-one calculation of finding square numbers using the multiplication method.

Step 1: First write down the given number.
        
72

Step 2: Multiply the given number twice using the sign .

  72 
x72

Step 3: Multiply the one digit (2) of the bottom with each digit of the top (72).

2 x 2 = 4 
2 x 7 = 14 

Step 4: Multiply the tens digit (7) of the bottom with each digit of the top (72).

7 x 2 = 14
7 x 7 = 49, then add the carry-over 1 (from the 14): 49 + 1 = 50.

Step 5: Arrange the results based on place value and add them.

Result from 2 x 72 = 144

Result from 7 x 72 = 5040

Step 6: Add the two results together.

72 × 72 = 144 + 5040 = 5184

Step 7: The total is, 5184

So, the square of 72 is 5184.

By this approach, the calculation is simplified using the square formula a2 + 2ab + b2, making it easier to understand and solve.

Step 1: Squaring a number (a²), means multiplying the number by itself:

a2 = a x a

Here, a = 72. So:

72² = 72 x 72

Step 2: Then break 72 into smaller numbers (expanded form)

72² = (70 + 2)²

Step 3: Use the square expansion formula 

(a + b)²  = a² + 2ab + b²

(70 +2)² = 70² + 2 (70) (2) + 2²

Step 5: Now, calculate each part 

(72)² = 4900 + 280 + 4

Step 6: Add them together 

4900 + 280 = 5180
5180 + 4 = 5184

Therefore, the square of 72 is 5184

To calculate the square of 72 using a calculator, you can follow simple steps to find the answer quickly. 

Step 1: Enter 72 on the calculator

Step 2:  Press the square button if available, or manually press the  (multiplication) button.

Step 3: Press the enter button. The calculator will show the answer 5184.

Therefore, the square of 72 is 5184.

• The square number of an even number is always even.

• When the final digit of an integer is either 1 or 9, a square number will finish with 1.

• If an integer's last digit is either 4 or 6, its square number will end with 6, if the integers are positive. 

• The square of an odd number will always be an odd number, and the square of an even integer will always be an even integer.

• Always remember that a number is not a perfect square if its square root is a fraction (or be it a decimal number). For example,√0.25 = 0.5, hence 0.25 is not a square number. 

• Integer: An integer is a whole number. It can be zero, negative, and positive. For e.g., -2, 2, and 0 are all integers.

• Square Root: Square root of a number is a value that when multiplied by the number itself gives the actual number. For e.g., square root of 36 is ±6.

• Decimal Number: A decimal number is one of the types of number which consists of a whole number and a fractional part. For e.g., 1.4367 where 1 is a whole number and 0.4367 denotes the fractional part. 

• Odd Number: It cannot be divided by 2 and will always leave with a remainder. For e.g., if 5 is divided by 2, we get 2 as a quotient and 2 as a remainder.

• Exponential Form: In mathematics, repeated multiplication is represented by exponential form. That is writing x  x as x2. Where x is raised to the power of 2, which means to multiply the given number twice or two times.

• Order of Operations (BODMAS): A rule that specifies the steps to solve an equation one by one. This includes parentheses, exponents, division, multiplication, addition, and subtraction.