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Intro to square roots

Learn about the square root symbol (the principal root) and what it means to find a square root. Also learn how to solve simple square root equations.

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• How can you get the square root of 4? You can't do 1^2, right? Cause that just equals 1. Or am I doing it wrong?
• Square root of 4 is 2.
An easier way to solve the square root for small and simple numbers like 4 is to just see which number, when multiplied twice with itself come up with the number.
ex) Solve the square root of 9,
1 times 1 = 1
2 times 2 = 4
3 times 3 = 9.
• Is there such thing as a triangle root?
• There is no such thing as a triangle root, however, there is such a thing as a cube root, which would be somewhat the same idea. You will learn about cube roots a little later.
• If we consider square roots as real numbers then can it be further classified in both rational and irrational numbers? why we need negative root 9 = -3 as we can also write root 9= 3 as well as -3?
• Yes, square roots can create 2 answers -- the positive (principal) root and the negative root. When you are working with square roots in an expression, you need to know which value you are expected to use. The default is the principal root. We only use the negative root when there is a minus in front of the radical.
For example:
8 + sqrt(9) = 11
8 - sqrt(9) = 5
• so are we dividing a number by it self?
(1 vote)
• No because if you divide a number by its self like 10 ÷ 10 then you would get 1 but the square root of 9 is 3 and if you were dividing a number by it's self then all the square roots would be 1.
• what is the square root of -1?
• This whole thing is kinda confusing for me. Can someone explain?
• The name kind of describes it. You’re basically finding the length of the side of a square if you know the area. For example, the square root of 121 is 11 because 11*11 is 121.
• What could you describe the difference between of Square root and Cube root?
• Cubing simply means multiplying by itself twice. If you think of a number as a line, then squaring gives you the surface area of the square with that line as its side. In that same way, we can construct a cube with side lengths of our initial number. Its volume is the "cube" of that initial number.

Once we get this, it's easy to reverse the process and understand the cube root: we take a number that represents the volume of a cube. When we construct the cube, the side length is the cube root of our number.

Therefore, if we take a number, construct the cube, and take its cube root, we get the original number back, which means we now can do this process both ways!
(1 vote)
• Why do numbers have both a positive and a negative square root?
• Square roots can be both because the factors are the same number and same value, and also because positive*positive = positive squared and negative*negative = negative squared.
(1 vote)
• Isn't a negative square root an imaginary number?
• Only if the minus sign is inside the square root.
sqrt(-9) creates the complex number 3i
-sqrt(9) just equals -3.

Hope this helps.
(1 vote)
• Is there a difference between Principle and Perfect square roots?