Question

How to subtract with fraction square roots.?

Answer 1

I'm doing a retest on mathematics so I'm reviewing/rejuvenating my brain.

Answer 2

Give an example.

Answer 3

\[2^{5/2} - 2^{3/2} \]

Answer 4

the answer comes out to 2^{3/2}, but I am so stumped on how to get that.
I keep getting "1" as my answer

Answer 5

Ah, and I meant exponents.
I just noticed that

Answer 6

Is it subtraction or division?

Answer 7

subtraction

Answer 8

one way to do this is factor out 2^(3/2)

Answer 9

\[ 2^{\frac{5}{2} } - 2^{\frac{3}{2} } \\
2^{\frac{3}{2} }\left( 2^{\frac{2}{2} } -1\right)
\]

Answer 10

I'm confused on how you got 2 ^(1/2)

Answer 11

Ignore it. Error.

Answer 12

notice that 2/2 is 1
so you have
\[ 2^{\frac{3}{2} }\left( 2^{1 } -1\right) \\
2^{\frac{3}{2} }\left( 2 -1\right) \\
2^{\frac{3}{2} } \cdot 1\\
2^{\frac{3}{2} }
\]

Answer 13

Ahh, I'm lost.
I get 2^(5/2) - 2^3/2) = 2/2 (1)
but where did the 2^(3/2) come in, shouldn't it have canceled out.?

Answer 14

*** I get 2^(5/2) - 2^3/2) = 2/2 (1) ****

undo your thoughts on that... that is not right.

do you agree that
\[ 2^{\frac{5}{2} }= 2^{\frac{3}{2} } \cdot 2^{\frac{2}{2} } \]?
the idea is multiplying terms with the same base (2 here) means we add their exponents

Answer 15

\[2^{5/2}-2^{3/2}=2^{3/2}\left(2^{2/2}-1\right)=2^{3/2}(1)=\sqrt{2^3}=2 \sqrt{2} \]

Answer 16

Okay,
I agree, but I still don't understand the 2^(3/2)

Answer 17

now we use that fact to write
\[ 2^{\frac{5}{2} } - 2^{\frac{3}{2} } \\
2^{\frac{3}{2} } 2^{\frac{2}{2} }- 2^{\frac{3}{2} }
\]

Answer 18

but wouldn't you subtract the "2" from each other.?

Answer 19

you have the same (ugly ) number in both terms: \( 2^{\frac{3}{2} }\) that you can factor out

can you do that ?

Answer 20

*** but wouldn't you subtract the "2" from each other.? ***

with numbers with exponents, we can't subtract or add them (except by changing them into decimal numbers). You have to think multiply (or factor out)

Answer 21

\[ 2^{\frac{3}{2} } 2^{\frac{2}{2} }- 2^{\frac{3}{2} } \]
factor out \( 2^{\frac{3}{2} } \) from both terms

Answer 22

how would I factor exponent fractions.?

Answer 23

@gjhfdfg

Cam you factor out b in a*b + b ?

Answer 24

you don't.

Instead think of 2^(3/2) as a number just like 7
if the problem was
7 * 2^1 - 7
could you factor out the 7 ?

Answer 25

You can't factor 7.?

Answer 26

unless the number is a .43243 etc

Answer 27

here is how factoring works:

if you have the same "thing" in two terms, like for example

7 * X + 7*Y
you can factor out the 7 (it is in both terms)
you get
7(x+Y)

if you distribute the 7, you get back what you started : 7X + 7Y

Answer 28

Okay not what I thought was factoring,

Answer 29

if you have
\[ 7 \cdot 2^{\frac{2}{2} } - 7 \]
which may be thought of as
\[ 7 \cdot 2^{\frac{2}{2} } - 7 \cdot 1 \]
you take the 7 out of each term and get
\[ 7 (2^{\frac{2}{2} }-1) \]

Answer 30

now do the same thing, except instead of 7 you have \( 2^{\frac{3}{2}} \)

Answer 31

not clear ?

Answer 32

I give,
I'm so lost.
But I appreciate your help.!

Answer 33

This is a tricky question, but the ideas are not hard to follow. But you have to know a few facts.

Do you agree that
2*3 + 2*5 = 16 ? ( I assume you agree)
notice that 2( 3+5) (or 2* 8 also = 16)

the idea is that 2*3 + 2*5 is the same as 2*(3+5)

Answer 34

now it turns out that rule works for lots of things other than nice numbers

2* hairy + 2 * complicated = 2*(hairy + complicated)

we use this same rule on
\[ 2^{\frac{3}{2} } 2^{\frac{2}{2} }- 2^{\frac{3}{2} } \cdot 1\]

we factor out the \(2^{\frac{3}{2} } \) from both terms
and write it as
\[ 2^{\frac{3}{2} } ( 2^{\frac{2}{2} }-1) \]

Answer 35

Aha, I agree that 6 + 10 = 16.

I'm just not familiar with much factoring.
The only factoring I can remember doing in my high school years were basic 2*2*3 = 12 & so on..

Answer 36

and 2^(2/2) - 1 would be subtracting 1 from 1 right.?

Answer 37

For the moment, accept that "factoring" means what I posted.
then you get
\[ 2^{\frac{3}{2} } 2^{\frac{2}{2} }- 2^{\frac{3}{2} } \cdot 1 \\
2^{\frac{3}{2} } ( 2^{\frac{2}{2} }-1)
\]

now what is \(2^{\frac{2}{2} }\) ?
the first step is what is 2/2 ?

Answer 38

2/2 is 1
so we can say
\[ 2^{\frac{2}{2}} = 2^1 \]

Answer 39

Okay,
so that leaves 2^(3/2) (2^1)

Answer 40

we started with
\[ 2^{\frac{3}{2} } ( 2^{\frac{2}{2} }-1) \]
we know
\[ 2^{\frac{2}{2}} = 2^1 \]

Answer 41

but then would that equal 1 * 2^(3/2) ?

Answer 42

yes, we get
\[ 2^{\frac{3}{2} } ( 2^{\frac{2}{2} }-1) \\
2^{\frac{3}{2} } ( 2-1)\\
2^{\frac{3}{2} } \cdot 1
\]

but 1 times anything is anything. We get
\[ 2^{\frac{3}{2} } \]

Answer 43

Ok,
I believe I get it....

Answer 44

Here is a short video on factoring
http://www.khanacademy.org/math/algebra/multiplying-factoring-expression/Factoring-simple-expressions/v/factoring-and-the-distributive-property-2

Khan has lots of videos on math. If you have a question, you can try searching his site for a video that explains it.

Answer 45

Oooh great thanks.!