Question

(√8x^2)(√2x^5)
A) 2x^3 √2x
B) 2x^2 √x
C) 3x^4 √x
D) 4x^3 √x

Answer 1

\(\color{#000000 }{ \displaystyle \sqrt{8x^2} \cdot \sqrt{2x^5} }\)

like this?

Answer 2

yes

Answer 3

they confused me alot

Answer 4

You know that; \(\color{#000000 }{ \displaystyle \sqrt{~\rm B~} \cdot \sqrt{~\rm C~}=\sqrt{~\rm B~\cdot~C~}}\)

Answer 5

So, you can use that at first,

\(\color{#000000 }{ \displaystyle \sqrt{8x^2} \cdot \sqrt{2x^5}\Longrightarrow \sqrt{16x^7}}\)

Answer 6

are you with me so far?

Answer 7

yes

Answer 8

Ok, good.

Answer 9

\(\color{#000000 }{ \displaystyle \sqrt{16x^7}=\sqrt{16}\cdot \sqrt{x^6}\times \sqrt{x^\color{white}{1}}}\)

Answer 10

can you tell me what the first two terms in the product will simplify to?

Answer 11

16 and x^6?

Answer 12

what is the square root of 16?

Answer 13

4

Answer 14

So, so far we can write

\(\color{#000000 }{ \displaystyle \sqrt{16x^7}=4\cdot \sqrt{x^6}\times \sqrt{x^\color{white}{1}}}\)

Answer 15

And then, tell me what is \(\color{#000000 }{ \displaystyle \sqrt{x^6}}\) ??

knowing that
\(\color{#000000 }{ \displaystyle x^6=x^{3+3}=x^3\cdot x^3=\left(x^3\right)^2}\)

Answer 16

(You know that \(\sqrt{49}=7\), because \(7^2=49\), right?)

Answer 17

yes

Answer 18

and so, you can tell me what is \(\color{#000000 }{ \displaystyle \sqrt{x^6}}\),

once you know that \(\left(x^3\right)^2=x^6\)

Answer 19

power of power right

Answer 20

well, usually, (for positive z), you have:

\(\color{#000000 }{ \displaystyle \sqrt{z^2}=\sqrt[2]{z^2} }\)
(the sides are the same... i.e., when the number in the corner of the root is unspecificed, it is always a 2)

\(\color{#000000 }{ \displaystyle \sqrt[2]{z^2} =z^{2/2}}\)
(Because there is a rule: \(\color{#000000 }{ \displaystyle \sqrt[n]{a^m} =a^{m/n}}\))

\(\color{#000000 }{ \displaystyle z^{2/2}=z^1=z}\)
(because the 2's cancel)

Answer 21

You have the same thing in \(\color{#000000 }{ \displaystyle \sqrt{x^6} }\),
except that \(z\), in your case, and as you can easily notice, is \(x^3\).

Answer 22

(I will explain later, why \(x\) is assumed to be positive, in your question)

Answer 23

\(\color{#000000 }{ \displaystyle \sqrt{8x^2} \cdot \sqrt{2x^5}= \sqrt{8x^2\cdot 2x^5}}\)

\(\color{#000000 }{ \displaystyle \sqrt{8x^2\cdot 2x^5}=\sqrt{16x^7}}\)

\(\color{#000000 }{ \displaystyle \sqrt{16x^7}=\sqrt{16}\cdot \sqrt{x^6}\cdot \sqrt{x~}}\)

\(\color{#000000 }{ \displaystyle \sqrt{16}\cdot \sqrt{x^6}\cdot \sqrt{x~}=4\cdot \sqrt{x^6}\cdot \sqrt{~x}}\)

So so, far we have simplified, till
\(\color{#000000 }{ \displaystyle 4\cdot \sqrt{x^6}\cdot \sqrt{~x}}\)

Answer 24

yes and sry i get confused even if im in 10th with this

Answer 25

\(\color{#000000 }{ \displaystyle \sqrt{x^6}=\sqrt[2]{x^6}}\)

(Remember what I did, \(\sqrt[n]{a^m}=a^{m/n}\))

\(\color{#000000 }{ \displaystyle \sqrt[2]{x^6}=x^{6/2}=x^?}\)

Answer 26

So, tell me
\(\color{#000000 }{ \displaystyle \sqrt{x^6}=x^?}\)

Answer 27

x^3

Answer 28

yes

Answer 29

therefore,

\(\color{#000000 }{ \displaystyle 4\cdot \sqrt{x^6}\cdot \sqrt{~x}=4\cdot x^3\cdot \sqrt{x~}}\)

Answer 30

So, do you understand all of the steps that we preformed to get the answer?

Answer 31

i getting it

Answer 32

it d

Answer 33

Yes

Answer 34

And now I will explain what's not precise about the question

Answer 35

have you heard about the "absolute value" ?

Answer 36

yes

Answer 37

Yes, and the absolute value (of z) is defined as,
\(\color{#000000 }{ \displaystyle \left|z\right|=\sqrt{z^2}}\)

And therefore,
\(\color{#000000 }{ \displaystyle \sqrt{x^6}=\sqrt{\left(x^3\right)^2}=\left|x^3\right| }\)

Answer 38

So, really the precise answer is,

\(\color{#000000 }{ \displaystyle 4\left|x^3\right|\sqrt{~x}}\)

Answer 39

But, the assumtion made is that \(x\) is NOT NEGATIVE.
And therefore, for non-negative \(x\), we have
\(|x|=x\) and \(\left|x^3\right|=x^3\).

Answer 40

can we be friend

Answer 41

What exactly do you mean by being friends?

((I'm usually friendly with people on the site, but actually making "friends" is something I very rarely do))

Answer 42

me too be i alway like to be friend wit ppl smart than me or nice

Answer 43

so it a no right

Answer 44

Well, I just hardly imagine online friendships...

Answer 45

usually my friendships are all face to face.

Answer 46

i did it that how i met my boyfriend thought online and all my friend i had stop being my friend so onlyi hhave online friend and some pal friend

Answer 47

idk ... will see how everything goes.

Answer 48

ok do u have fb mine candyquinnred

Answer 49

im a girl also because my picis of me and my bf