Find the square of 42.2.
Let’s start by reminding ourselves that we can write the square of a number, for example the square of 𝑥, as 𝑥 squared, which is equal to 𝑥 multiplied by 𝑥. Here, we’re asked to find the square of the decimal number 42.2. And we do this in exactly the same way as we would for an integer or another type of number or a variable. So, let’s work out the value of 42.2 times 42.2.
To multiply a decimal number, we first consider our values as whole numbers. Here, we have 422 times 422. And then, we restore the decimal point into our answer at the end. We can use any multiplication method, but here we’re going to use the grid method. Starting with 400 times 400, this would be 160000. 400 times 20 will give us 8000. And 400 times two will give us 800. And we can complete the rest of the values in the grid.
Then, we need to add up the values that we’ve worked out. Here, I’ve added the columns first, but you can add the rows first if you prefer. And adding our column totals will give us our answer of 178084. Notice that this is our answer to 422 squared, and not 42.2 squared. So, we need to restore our decimal point. To find where the decimal point goes, we count the decimal digits in the numbers we’ve multiplied.
So, now, we know that our answer will have two decimal place digits. Therefore, using our answer to 422 times 422, we have the digits one, seven, eight, zero, eight, four, and we know that we must have two decimal place digits. This means that our decimal point will go between the zero and the eight. So, our answer for the square of 42.2, we can say as 1780.84 or 1780 and eighty-four hundredths.