ROOTS

This is the roots page! Seperated from the Fundamental Arithmetic page because well, it is not that common in beginner math. Roots are referred to by the symbol √ (radical/root).

So, lets start. Do you know how addition is the opposite of subtraction, division is an inverse operation to multiplication? Well, roots are the opposite to exponents! When you're using roots, you're basically thinking, "What number, when multiplied by itself a certain number of times, gives you this original number?". For example...

• 3^2 means 3x3=9
• 2^3 means 2x2x2=8
• Roots undo this process, so you're seeing which number equals the number you want to root!

So if you see a square root (meaning the opposite of ^2) like √9, thats 3, because 3x3 is 9!

There are also different types of roots, not just square roots. Here is a list of some of them!

• Square root (√) asks what number multiplied by itself 2 times gives the answer. (example: √16=4 because 4×4=16)
• Cube root (∛) asks what number multiplied by itself 3 times gives the answer. (example: ∛27=3 because 3x3x3=27)
• Higher roots like 4th root, 5th root and so on are the same idea, just more repetitions.

Another way to connect roots to exponents is that they're actually just exponents as fractions. √a is the same as a^1/2 and ∛a is the same as a^1/3. This is why roots and exponents are tightly linked, it's because they're two directions of the same idea!

If you want even more about roots, look at this video from math antics.

Bonus Tip: Not all roots are perfect. Roots that give whole numbers like √4=2 are perfect squares (and ∛27 is a perfect cube!), but some numbers give some weird results. For example, √2=1.41421356237... it continues forever. The approximate form is 1.414.

Now you know all about roots!