Main content

# Understanding square roots

Learn how square root means what number multiplied by itself will result in the given number. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- Is it like finding 10% of a number? I'm kind of confused with that a little...(7 votes)
- no,to find the square root, you need to find what times itself is equal to the number under the radical(11 votes)

- what does one do if they are adding two square roots, such as the square root of 13 + the Square root of 13?(9 votes)
- In this case the square roots behave like algebra. let √13 be a, then a + a = 2a , substitute a with 13 and you get the answer ; 2√13.

If you use a calculator then; (√13 + √13) = 2√13 = 7.21110255093.

The above question is 7 yrs old, but if anyone has the same question, please learn indices if you want to know more: Here's a link https://www.khanacademy.org/math/mr-class-7/x5270c9989b1e59e6:indices(4 votes)

- Is there is a trick or shortcut into finding the answer of a square root, other than guess and check?(4 votes)
- Most square roots are irrational, meaning that their decimal form continues forever without a repeating pattern. If you are trying to take the square root of a number that is not a perfect square, the best you can hope for is an approximation. You are usually best served to use a calculator to get these results, but there is a method I enjoy for approximating square roots. It is an iterative method developed by Heron of Alexandria, an ancient Greek engineer.

First, guess a convenient value for the square root. Divide the number by your guess. Now you have two numbers that multiply to get your original number. Take the average of these two numbers. This becomes your second guess for the square root. So again, you can divide the original number by this new guess, and take the average of these two numbers to get a third guess, and so on. Soon consecutive guesses will not change much. This is the approximation of the square root.(13 votes)

- So the square root of a number is the number that when you multiply it by itself is equal to that number?(5 votes)
- Yes. Go to0:40in the video to learn more.(3 votes)

- So, is this how every "square root" is? Im a little confused...(3 votes)
- Yeah think about a square root as the number you get when you multiply something by itself.

Helps to think about the definition of multiplication as adding a number to itself:`2 x 3 = 2+2+2 = 3+3 = 6`

Exponents are similar, except now we're**multiplying**the number to itself instead of**adding**it.`2^2 (squared) = 2 x 2 = 2+2 = 4`

3^2 (squared) = 3 x 3 = 3+3+3 = 9

Taking the square root is figuring out what number**multiplied**by itself is equal to the number under the square root symbol.

So:`√4 = 2, because 2*2 OR 2^2 = 4`

√9 = 3, because 3 x 3 = 9 OR 3^2 = 9

Hopefully that helps!(4 votes)

- What will we use square roots for?(5 votes)
- Square roots will be required for a lot of things like transformations, graphing, trigonemetry(4 votes)

- My dad told me that if we need to find the square of a number it will be easy if we know the square of the last number.The difference between one square and the next square is the sum of their square roots.

eg:-to find the square of 7

just add 6 and 7 to six square ie 36

36+6+7

=49 ie the square of 7(4 votes)- It's true, but there's a more general formula.

(x+1)^2= x^2+2x+1

For an example, we know that 100 squared is 10000, right? Well, 101 squared is (100+1)^2. That leads us to 100^2+2(100)+1, and the answer is- Finally-

10201. That's the result of 101 squared!(4 votes)

- How would you find the square root of non-perfect squares?(4 votes)
- What happens when the equation is (-8)^-2/3(3 votes)
- The denominator of the exponent is telling you to do a cube root. The numerator is telling you to square the number.

You can do them in either order. Personally, I prefer to do the cube root first because I can work with smaller numbers.

Cube root(-8)=-2

Then square the -2: (-2)^2 = 4

Hope this helps.(4 votes)

- whats a square root(3 votes)
- A square root is a number that when multiplied by itself makes a specified quantity. For example 3, when 3 is multiplied by itself (3*3) it equals 9, thus making 3, the square root of 9.(3 votes)

## Video transcript

We're asked to find the
square root of 100. Let me write this down bigger. So the square root is this
big check-looking thing. The square root of 100. When you see it like this,
this means the positive square root. If you're familiar with negative
numbers, you know that there's also a negative
square root, but when you just see this symbol, that means
the positive square root. So let's think about what
this is saying. This is asking us find the
number, the positive number, that when I multiply that number
by itself, I get 100. So what number when I multiply
it by itself do I get 100? Well, let's see, if I multiply
9 by itself, that's only going to be 81. If I multiply 10 by itself,
that is 100. So this is equal to-- and let
me write it this way. Normally, you could
skip this step. But you could write this as
the square root of-- and instead of 100, 100 is the same
thing as 10 times 10. And then you know, the square
root of something times itself, that's just going
to be that something. This is just equal to 10. So the square root
of 100 is 10. Or another way you could write,
I guess, this same truth is that 10 squared, which
is equal to 10 times 10, is equal to 100.