Question

Can someone please help me with simplifying square roots?
Pretty please, with a rainbow cupcake on top? :3
Any assistance is greatly appreciated! <3

Answer 1

\(\Large\bf\color{blueviolet}{Simplify:}\)

\(\Large\sqrt{72}\)

Answer 2

I really don't get the concept of square roots in general, but I know that to simplify, you need to take out something called "perfect squares"?

Answer 3

factor the 72 into primes, and look for pairs of numbers that you can "take out"

Answer 4

a simple example
\[ \sqrt{4} = \sqrt{2\cdot 2} = 2 \]
or
\[ \sqrt{8} = \sqrt{2\cdot 2\cdot 2} = 2\sqrt{2} \]
this last example has a pair of 2's that come out, and 1 2 left over that stays inside.

Answer 5

for 72, I would divide by 2 to get
2*36
now divide the 36 by 2 to get
2*2*18
keep going ?

Answer 6

I can somewhat get it.
I get how you got 36 and 18.

Answer 7

I would learn (some) of these divisibility rules
https://en.wikipedia.org/wiki/Divisibility_rule#Divisibility_rules_for_numbers_1.E2.80.9320
I would learn as many of the primes as you can:
http://metricconversion.biz/list-of-first-100-prime-numbers.html

Answer 8

So, each time you divide, you just add a 2 to multiply by, correct?

Answer 9

do you agree that
2*36 = 72 ?

now look at 36. it is even, so it is divisible by 2: and 36= 2*18
that means
2*36 can be written as 2*(2*18) or 2*2*18 (and if you multiply it out you get 72)
now 18 is even, so we can divide it by 2: 18 = 2*9
replace 18 with 2*9
and our list is now
2*2*2*9

Answer 10

9 is divisible by 3 : 9= 3*3
so the list is
2*2*2*3*3
if you multiply that out , you get 72
2 and 3 are prime (nothing divides into them
so we are done factoring
now circle pairs of the same number.

Answer 11

Okay, I'm starting to get it..

So, would it be
2^3*3^2 ?

Answer 12

yes you can write it like that (easier, especially for 2^10 , for example)
but for these problems, I would stick with
2*2*2*3*3
and circle one pair of 2's and one pair of 3's
(leaving a unmatched 2 , which stays inside the square root)

Answer 13

Okay, but there's no square root symbol at the end, though. o-O

This is how my math teacher showed it (which I wasn't getting)
\(\sqrt{12}\) = \(\sqrt{4}\) \(\sqrt{3}\) = \(\large2\) \(\sqrt{3}\)