Question

Please explain how to solve the following roots.

Answer 1

\[\sqrt{27}\]

Answer 2

That is equivalent to 3*sqrt3

Answer 3

So how is the answer \[\sqrt[4]{2}\]

Answer 4

That is the answer i got at least.

Answer 5

idk how you got that

Answer 6

\[\sqrt{27} = \sqrt{ 9 \times 3 } = \sqrt{ 9 } \times \sqrt{3} = 3\sqrt{3}\]

Answer 7

Me neither.

Answer 8

there is no root 2 in the prime factors of 27

Answer 9

That's what I thought the answer would be. What about this one? Can you check my answer for it?

Answer 10

\[\sqrt{32}\]

Answer 11

ah, now that's 16*2 = 4 root(2)

Answer 12

\[\sqrt{32}=\sqrt{16x2}=\sqrt{8x2x2}=\sqrt{4x2x2x2}=\sqrt{2x2x2x2}= 2\sqrt{4}\]

Answer 13

tssss

Answer 14

\[\sqrt{32} = \sqrt{ 16 \times 2 } = \sqrt{16} \times \sqrt{2} = 4 \sqrt{2}\]

Answer 15

Oh. Well then how about this one. \[\sqrt{40}=\sqrt{4x10}=\sqrt{2x2x5x2}=5\sqrt{4}\]

Answer 16

it's ok up to 4x10

Answer 17

agfter that\[\sqrt{4} \times \sqrt{10} = 2 \sqrt{10}\]

Answer 18

You are looking to break down a number into the product of a "good square" ( like 4,9,16,25,36 etc) and anohter number

Answer 19

I am totally not understanding this.

Answer 20

ok, hold on

Answer 21

lets look at \[\sqrt{40}\]

Answer 22

We want to break that 40 into 2 pieces

Answer 23

one piece has to be a square the other doesnt matter

Answer 24

You know what a square is?

Answer 25

no

Answer 26

ok, a square is a number multiplied by itsself.

Answer 27

\[1^2 = 1 \times 1 = 1\]

Answer 28

\[2^2 = 2 \times 2 = 4\]

Answer 29

got it

Answer 30

so the squares (up to 10 are) 1,4,9,16,25,36,49,64,81,100

Answer 31

what you want to do with the number under the root sign is break it up into 2 parts, 1 square, the other not

Answer 32

\[\sqrt{40}\]

Answer 33

we have 40, that breaks down into 4 * 10

Answer 34

yes

Answer 35

with 4 being the sqaure and 10 being not a square

Answer 36

ok

Answer 37

you're always looking for the largest square to fit

Answer 38

like with
\[\sqrt{32}\]

Answer 39

32 breaks down into 4x8 but also 16x2

Answer 40

you want to choose 16x2

Answer 41

after that, you can break up the root sign, and simply take the root of the square

Answer 42

and voila, you're done

Answer 43

\[\sqrt{40} = \sqrt{4 \times 10 } = \sqrt{4} \times \sqrt{10} = 2 \times \sqrt{10} = 2 \sqrt{10}\]

Answer 44

the \[\sqrt{4} = 2\]

Answer 45

ok so 40 would be 4*10=2*2*5*2= \[5\sqrt{2}\]

Answer 46

nope, 40 = 4*10, you dont break in into any more pieces

Answer 47

40 = 2 * 2 * 2 * 5 of course, but that doesnt really help

Answer 48

So I am making this more complicated then this has to be?

Answer 49

you need to break it into 2 pieces, 1 piece a nice square, the other just a number

Answer 50

you're doing too much, yeah, and in the process you're confusing yourself

Answer 51

Oh my gosh. I feel so stupid.

Answer 52

another example, try \[\sqrt{50}\]

Answer 53

nah, dont feel stupid for trying. People who don't try are stupid

Answer 54

:) The answer is 10x5= \[10\sqrt{5}\]

Answer 55

almost right

Answer 56

it's 25*2 , can you give me the answer now?

Answer 57

\[25\sqrt{2}\]

Answer 58

\[\sqrt{50} = \sqrt{25*2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}\]

Answer 59

almost right again, you need to root the 25

Answer 60

\[5\sqrt{2}\]

Answer 61

yup
that's the only trick you'll need for this kind of questions

Answer 62

\[\sqrt{32}=16x2=16\sqrt{2}=8\sqrt{2}\]

Answer 63

almost right

Answer 64

\[\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4 \sqrt{2}\]

Answer 65

cause \[\sqrt{16} = 4\]

Answer 66

not 8

Answer 67

i gotto go eat now, kids are screaming they're hungry ;)

Answer 68

I thought that was the answer. Thank you SO much for your help! I am going to try this on my own now. Bye! :D