Question

Can someone please help me understand how to find the square root of 90? I am just learning about radicals and stuff so I am very confused.

Answer 1

ok

Answer 2

do you know half of 90 is

Answer 3

Have you learned about exponents yet?

Answer 4

half of 90 is 45

Answer 5

ok so now

Answer 6

Um do you mean the properties of exponents? If so I have but, I do get confused on it often

Answer 7

you pretty much solved it however

Answer 8

ok but, I actually need the steps on how to do this because hold on I'm going to post something from my lesson that I do not understand

Answer 9

if your trying to get 90 times it slef

Answer 10

ok

Answer 11

Here are two ways the square root of 32 can be simplified.

√32=√4•8=√4•4•2=√4•√4•√2=2•2•√2=4•√2=4√2

√32=√2•16=√2•√16=√2•4=4√

Answer 12

uh whats with all the black question marks

Answer 13

OMG what happened to my post lol it turned into diamonds with question marks in them!!!

Answer 14

Let me add one thing here, the radical is just an exponent, if you know exponent properties, this whole thing makes more sense

Answer 15

ok

Answer 16

@FibonacciChick666

Answer 17

help him

Answer 18

i need to attend someone else

Answer 19

excuse me I'm a girl lol

Answer 20

oh sorry

Answer 21

it's ok! :)

Answer 22

you had an animal picture

Answer 23

ok, so, let's talk about exponents, do you remember the properties of them (like when you multiply x^a*x^a what do you get?

Answer 24

um like power of a power and quotient of a power property?

Answer 25

yes that's it that's what I learned about

Answer 26

properties of exponents

Answer 27

ok, so a radical, is just a fractional exponent

Answer 28

exponents aare kind of easy and sometimes fun...

Answer 29

if you have a cube root for example, the exponent is just 1/3,

Answer 30

ik a great source of help.

Answer 31

brb

Answer 32

@hero

Answer 33

what is it?

Answer 34

the nice thing is that once you do that, you can use the distributive property to figure out the answer

Answer 35

ok

Answer 36

so in your case you have:\[\sqrt{90}=90^\frac{1}{2}\]

Answer 37

ok why did you put 1/2?

Answer 38

you can also write that as \[(90)^\frac{1}{2}\] Becaus you have a square root, there is a little implied two that would sit outside the radical where you usually see a 3 or 4 etc

Answer 39

ok so now what do I do?

Answer 40

according to the example in my lesson they did something like this:

Answer 41

hold on going to post the example

Answer 42

so no, you want to factor 90, into it's prime factorization ( ie only use multiplication of 2,3,5,7,11...)

Answer 43

so the best was to do that, is to start by dividing your number by 2, so what is 90/2?

Answer 44

I don't need the example it's ok

Answer 45

ok

Answer 46

45

Answer 47

so the best way** to do that, is to start by dividing your number by 2, so what is 90/2?

Answer 48

i feel so accomplished i helped the kid get a 100 on his test :) ok now your turn.

Answer 49

45

Answer 50

ok so now, you have \[(2*45)^\frac{1}{2}\]

Answer 51

thats what square root is

Answer 52

ok

Answer 53

let's see what we can do with the 45 now, does that divide evenly by two?

Answer 54

square root can mean times it self sometimes so its kind of tricky.

Answer 55

no it doesn't

Answer 56

theres a decimal but tell us what it is

Answer 57

good, but what are the factors of it?

Answer 58

I don't want the decimal

Answer 59

no not yiu

Answer 60

ummmm... I don't know what you mean

Answer 61

factors of 45 sorry, what numbers can you multiply together to get 45?

Answer 62

ok so like what do you do with the 45

Answer 63

is what he means

Answer 64

9*5

Answer 65

...please, I got this.

Answer 66

perfect! animal

Answer 67

k fib tell me when you get stuck.

Answer 68

so now we have \[(2*5*9)^\frac{1}{2}\]

Answer 69

now, lets. rewrite the 9 somehow

Answer 70

do you follow to here?

Answer 71

yes I'm getting it

Answer 72

awesome, ok, so now, how can you write nine in terms of a prime number? (factors of 9)

Answer 73

3*3?

Answer 74

yep!!!

Answer 75

what is another way to write 3*3?

Answer 76

(think exponents)

Answer 77

3^2

Answer 78

purrrfect

Answer 79

now, you have \[(2*3^2*5)^\frac{1}{2}\]

Answer 80

so, how can you "simplify" the exponent? What property of exponents is useful here?

Answer 81

ie, when you have an exponent to a power, what do you do with the exponents?

Answer 82

I don't know because I have not really remembered my properties of exponents sorry

Answer 83

it's ok, check this out, then come back and it should be obvious: http://www.purplemath.com/modules/exponent.htm

Answer 84

ok

Answer 85

oh and what do you mean how can I simplify the exponent I am not too sure on what you mean about that

Answer 86

ok, so how can you distribute the 1/2 to each number in the parentheses?

Answer 87

you may like this page too http://www.purplemath.com/modules/exponent5.htm

Answer 88

that is what we are doing

Answer 89

I'll give you an example, you have \[(ab^ec)^d\] that is the same as

Answer 90

change it to a decimal?

Answer 91

\[a^db^{ed}c^d\]

Answer 92

nope, it's easier than that

Answer 93

how?

Answer 94

so notice in the example, the exponent outside was just multiplied all the original exponents inside the parentheses

Answer 95

it's just like simplifying \[(x^2)^3\]

Answer 96

where did the 2 and 3 come from?

Answer 97

that is just an example, how would you simplify that?

Answer 98

oh ok