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Estimating Square Roots - Concept

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

When a radical is not a perfect square (1, 4, 9, 16, ), estimating square roots is a valuable tool. When asked to estimate the value of a radical between two consecutive integers, find the two perfect squares that are slightly less and slightly more than the radicand. Also, remember that negative numbers do not have a real number square root.

Alright Math stars. What would you say if I asked you to tell me the square root of 16? Would you say 4? You'd be right, kind of. There's actually another number whose square the square root of 16 is also another number. Do you know what the other number is? -4. It's kind of tricky. In Math we usually deal with what we call the principle square root. The principle square root is the positive one. But don't forget that the square root of 16 could also be -4. Usually that'll be written like this. It'll say the negative square root of 16 to tell you we're looking for -4.
Sometimes you'll see plus minus. That means they want both answers, that means they want both answers, the positive and the negative version. 4 and the -4. But one thing to look out for is if you see this. If you have a negative sign under the square root, be really careful with that distinction. Under the square root is no real value or no real number because there's no square roots of negative numbers. Nothing times itself gives you a negative answer. So that's important to keep in mind when you're working with estimating square roots.
If you're asked to find the square root of something like 150, that's tricky. You know what the square root of 144 is but 150 is a little bit different. So when you're looking at estimating square roots, it's important that you guys are familiar with what we call perfect squares or square numbers. This is a list of them. This is 1 squared, 2 squared, 3 squared, 4 squared all the way up to 15 squared.
It's important that you guys get really familiar with this numbers and when you recognize them, something special happens in your head. Like whenever you see the number 49, you should be like, "Oh 49. That's 7 squared." Seven's probably involved with whatever you're about to do in your Math problem.
So when you're asked to estimate square roots, it's important that you know the perfect square numbers. Once I know the perfect square numbers, I can estimate pretty easily. Like earlier I mentioned the square root of 150. Well, 150 falls between these two perfect squares right? That's 12 squared and 13 squared. That tells me that the square root of 150 is somewhere in between the numbers 12 and 13. You're going to see some practice problems like that in your homework.

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