Squaring any 2-digit number

A guest post by Maria Rainier

Shortcut to Squaring Any 2-Digit Number

What do you do when your calculator has been confiscated and the world is depending on you to square a two-digit number within a minute? Don’t panic – just follow three simple steps that require basic addition and multiplication, and you’ll be able to solve the problem in no time. If you practice enough, you’ll even be able to complete each step mentally, rendering scratch paper unnecessary. This will save you time on drills and strengthen your skills so you can tackle other challenges. Eventually, you’ll be able to solve multi-step squaring problems without ever breaking a sweat – or a pencil.

This is a trick I learned during my old MATHCOUNTS days, but it comes in handy for lots of other competitive math as well. It was great for sprint, team, target, and countdown problems, but now it just comes as second nature whenever I run into a more complex problem that involves a squaring step. If you’re having trouble squaring two-digit numbers on the fly without a calculator, give this method a try. It seems a bit cumbersome at first, but as you practice, you’ll be able to speed up the process and get your answer within seconds.

3 Steps for 2-Digit Squares

Let’s work through the steps with an example to better demonstrate the process. Imagine that you’re expected to square 83 quickly and accurately – the following steps will help you complete the task.

1. Square each digit individually, making sure that you get a two-digit number for each square. If the number is low and its square gives you only one digit, use 0 as a placeholder.

8² = 64 and 3² = 9 = 09, giving you 6409

2. Now, multiply the two digits and double your answer, adding a 0 to the end.

8 X 3 = 24; 24 X 2 = 48, giving you 480

3. Simply add your answers from steps one and two.

6409 + 480 = 6889, or 83²

Bio: Maria Rainier is a freelance writer and blog junkie. She is currently a resident blogger at First in Education, where recently she’s been researching different online mechanical engineering degree programs and blogging about student life. In her spare time, she enjoys square-foot gardening, swimming, and avoiding her laptop.

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