Question

Simplifying Radicals, HELP PLEASE?

Answer 1

1) Sqr. Root of 96
2) 8square root of 63x^5
3) Sqr. Root of 128x^5y^2
4) power of 3 sqr. root of 32
5) power of 3 sqr. root of 56x^14

Answer 2

Please do not write in decimal form.. Thank you :D

Answer 3

Can you factor 96 into two numbers were one of those numbers is a perfect square?

Answer 4

Yes??? Idk.

Answer 5

ok give it your best shot and show me what you think it is

Answer 6

I don't know how to do it... Can you tell me how?

Answer 7

the list of perfect squares are

1, 4, 9, 16, 25, 49, 64, 81, 100, ..

and this list goes on

Answer 8

look familiar?

Answer 9

oops meant to say

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, ..

Answer 10

which of these numbers is a factor of 96?

Answer 11

no, just a factor

Answer 12

Um.. 1, 4, 16,

Answer 13

good, the largest factor in that list is 16

Answer 14

now divide 96 by 16 to get

96/16 = ???

Answer 15

6

Answer 16

so 96 is the same as 16*6

Answer 17

since 96 = 16*6

Answer 18

so this allows us to go from

\[\Large \sqrt{96}\]

to

\[\Large \sqrt{16*6}\]

Answer 19

Afterwards, we break up the square root to get

\[\Large \sqrt{16}*\sqrt{6}\]

Answer 20

Okay. Is that it?

Answer 21

not quite there though

Answer 22

can we simplify \(\Large \sqrt{16}\) ??

Answer 23

4?

Answer 24

good, so in the end,

\[\Large \sqrt{96} = 4\sqrt{6}\]

Answer 25

whoah whoah whoah.... what?

Answer 26

where are you lost

Answer 27

Why does the 4 go in front of the

Answer 28

here are the full steps

\[\Large \sqrt{96} = \sqrt{16*6}\]

\[\Large \sqrt{96} = \sqrt{16}*\sqrt{6}\]

\[\Large \sqrt{96} = 4\sqrt{6}\]

Answer 29

notice how we factored, broke up the root, then simplified any roots we could

Answer 30

Oh wait.. Nevermind. I get it! Thank you :)
Will you help me with the rest as well, please?

Answer 31

How about I show you how to do #2 and you show me how to do #3 (so you can show me that you have an idea of what's going on). Sound good?

Answer 32

Okay :) Thank you!

Answer 33

2) 8√(63x^5)

Answer 34

The same basic rule applies as before. We need to factor each expression where one of the factors is a perfect square.

So 63 = 9*7 (9 is the largest perfect square factor)

for x^5, we can rewrite/factor it to get x^2*x^2*x

This means...

\[\Large 8\sqrt{63x^5} = 8\sqrt{9*7x^2*x^2*x}\]

\[\Large 8\sqrt{63x^5} = 8\sqrt{9}*\sqrt{7}*\sqrt{x^2}*\sqrt{x^2}*\sqrt{x}\]

\[\Large 8\sqrt{63x^5} = 8*3*\sqrt{7}*x*x*\sqrt{x}\]

\[\Large 8\sqrt{63x^5} = 24x^2\sqrt{7x}\]

Answer 35

The big difference is that variables are now involved, but the same basic idea applies

Answer 36

I'm confused on the x^5 part.

Answer 37

x*x = x^2 right?

Answer 38

yes??

Answer 39

well x^2 times x^2 = x^4

and x^2 times x^2 times x = x^5

Answer 40

so that shows us that x^5 factors to x^2*x^2*x

Answer 41

oooh, okay. sometimes i need to see it in word form to know what's going on, lol.

Answer 42

i gotcha, well the star symbol * means "times"

Answer 43

so, give me a minute to figure this out real quick & see if i understand...

Answer 44

2*3 = 2 times 3

Answer 45

ok

Answer 46

why is that last part 24x^2 sqr. root 7x??

Answer 47

How do you know which x's go where & how many?

Answer 48

because I multiplied all the terms outside the root

Answer 49

8*3 =24

Answer 50

x*x = x^2

Answer 51

I know.. but why do they go there & not by the 7?

Answer 52

all the terms inside the roots are multiplied and combined under one single root

Answer 53

why is it not 7x^3 ?