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## Class 8 Math (Assamese)

### Course: Class 8 Math (Assamese)>Unit 5

Lesson 1: Square roots using factorisation

# 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...
• no,to find the square root, you need to find what times itself is equal to the number under the radical
• what does one do if they are adding two square roots, such as the square root of 13 + the Square root of 13?
• 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
(1 vote)
• So the square root of a number is the number that when you multiply it by itself is equal to that number?
(1 vote)
• Is there is a trick or shortcut into finding the answer of a square root, other than guess and check?
• 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.
• So, is this how every "square root" is? Im a little confused...
• 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 = 43^2 (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!
(1 vote)
• What will we use square roots for?
• Square roots will be required for a lot of things like transformations, graphing, trigonemetry
(1 vote)
• 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
• 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!
• How would you find the square root of non-perfect squares?
• Estimate it
(1 vote)
• What happens when the equation is (-8)^-2/3
• 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.