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How to Find the Square Root of a Number

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  • 0:03 Squares
  • 1:39 Square Roots
  • 2:25 Find the Square Root
  • 3:11 Practice
  • 5:10 Lesson Summary
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Lesson Transcript
Instructor: Jeff Calareso

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

What is a square root? In this lesson, we'll learn what a square root is and how to find it. We'll review a variety of examples in order to master the concept.

Squares

Did you ever grow a plant in a glass so you could watch its roots grow? Did you ever see roots grow into a perfect square? No? Me neither. And, in fact, plant roots growing into polygons have nothing to do with square roots.

So what are square roots? Before we can learn how to find square roots, let's quickly review squares. The square of a number is just a number multiplied by itself. If our number is n, then n to the second power is n squared. We'd write 3 squared like this:

3 squared
3 squared

The square just means it's raised to a power of two, or has an exponent of two, which means the same thing.

So why is it called a square? Imagine you're planting seeds in the actual ground - no glasses required. Let's say it's tomatoes. You want to form a square of tomato plants that's 3 by 3. That's one, two, three along the bottom below and one, two, three along the side.

This image explains why a number multiplied by itself is called a square.
image of garden in square blocks

How many plants will you have? 3 * 3, or 9. That's why a number multiplied by itself is called a square.

Some numbers are called perfect squares. 9 is one example. That means it's a number that you'd get by squaring a whole number. Start with 1. 1 is a perfect square; it's 1 * 1. Then 4, which is 2 * 2, then 9, then 16, 25, 36, 49, 64, 81 and 100. 100 is just 10 * 10. Perfect squares just keep going from there.

Square Roots

That leads us to square roots. A square root is the inverse of squaring a number. In other words, the square root of n^2 is n.

We use this symbol to indicate a square root:

The radical sign indicates a square root.
radical sign

This is called a radical sign. Radical isn't just a word used by '80s surfers and Ninja Turtles. In math, the word 'radical' actually means 'root.' And you know what? That line stretching down kind of looks like the root of one of our tomato plants diving into the ground.

This symbol doesn't always mean the square root, though. You might see one like the one below, with a number on it. This one is the cube root:

Cube root
cubed root

That's more advanced than what we're dealing with here, but know that if there's no number, then it's implied to be a square root.

Find the Square Root

Let's say we see this:

Square root of 4
square root of 4

We'd call this the square root of 4. We might also say root 4 or radical 4. All of those phrases mean the same thing. We want to know what number squared is 4.

Of course, we know that 2 * 2 = 4. So our answer here is 2. You might think of it like a tree. A huge oak tree grows from a tiny acorn. Likewise, the root of 4 is 2.

Now, 2 * 2 isn't the only way to get 4. What if we did -2 * -2? That's also positive 4. But positive 2 is called the principal root and, certainly at this level of math, we only consider positive 2 to be our answer.

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