So you ask what are Square roots
That is a good question and it’s actually simpilar then it looks but can’t be solved by a hand. Wait you can’t solve it by hand wouldn’t that make it harder? Well yes but it’s really quite simple.
  • √y is the same as saying something multiplied by it self is equal to y
  • so √(x * x) is the same as √y and it can also written as √(x²)
  • so now knowing y is x² and we can find x and then the square would cancel out the square root( √y = √(x*x) or √x² = x
  • Starting to rap your mind around this heres and example
  • √81 so we know a number multiplied by it self will get 81 what are they?
  • 9 multiples by it self gets 81. 81 = 9²
  • so now we plug that in for 81
  • √9²
  • now because squaring cancels out square roots we are left with 9 and that is the square root of 81.
Starting to get it?
Ok so that's all simple right what about negative numbers? That's the easy part the square root of a negative number is always i witch is also equal to -1. Oh now that's much easier.
So from here the only other thing you need to know is the other way of writing square roots which is:


Not to hard.

Here's some problems to practices. Remember order of operations for the hard ones.
easy
√144
√25
medium
√20
√12
hard
√(25*2)
√(100/2)



Jasmine Thomas

Review: Square Roots

Square root of 25

So knowing that a number multiplies itself to get 25 we can start by finding the multiples of 25 which is 5

5(5)=25 square root of 5^2

5 is the square root because sqaure rooting the problem cancels out squaring which leaves us with 5.






Stefen and Rob
pg.394
#1) 3√x+3=15
-3 -3
3√x=12
3 3
√x = 4
x = 4^2
x= 16


Roots

A number that is not negative that must be multiplied times itself to a equal a given number..


FX-70 Consider the examples below and check them in your head or on your calculator.
9²=81 and ²√81=9
8³=512 and ³√512=8
7⁵=16807 and ⁵√16897=7
Use these ideas to compute the following without a calculator.

a) ²√49=
b)⁴√81=
c)⁴√10000=
d)⁵√-32=

a) ²√49=7
7x7

b)⁴√81= 3
3x27
3x(3x9)
3x(3x(3x3))

c)⁴√10000= 10
10x1000
10x(10x100)
10x(10x(10x10))

d) ⁵√-32=
NOT POSSIBLE !
you cannot take the fifth, or any root for that matter, of a negative number.

Source: http://www.cpm.org/