Question

Multiply and simplify. Assume that all expressions under the radicals represent nonnegative numbers.
√3x^7 √18x

Answer 1

\[\sqrt a \times \sqrt b = \sqrt {ab}\]

Answer 2

I got until that \[\sqrt{54x^8}\]

Answer 3

and I got stuck

Answer 4

what is the square root of x^8?

Answer 5

2 I'm confuse with the square root and the whole thing

Answer 6

what happens when you square the number 4?

Answer 7

I don't really know what that means.. Sorry I'm kind of lost with this lesson

Answer 8

Recall the following identity for constants a and b:\[(x^a)^b = \underbrace{\left(\underbrace{x\times x \cdots}_{a \text{ times}}\right)\left(\underbrace{x\times x \cdots}_{a \text{ times}}\right)\cdots }_{b\text{ times}}=x^{ab}\]Now, apply this to the fact that\[\sqrt{x} = x^{\frac{1}{2}}\]

Answer 9

I gosh... I feel like you guys are talking japanese

Answer 10

Sorry...that got cut off. The right hand side says \[(x^a)^b = x^{ab}\]

Answer 11

familiapr - what is confusing to you?

Answer 12

the whole thing...I don't know what the square root is or how to get the square root
of a number

Answer 13

okay. familiapr, do you know what the area of a square is? say the side is of length 4

Answer 14

A square root is exponentiation to 1/2. Apply the formula I gave where your b=1/2. One way to think of a square root is that it outputs a number when squared will produce the original number. For instance\[\sqrt{64}=64^{\frac{1}{2}}=8\] because \[8^2=64\]

Answer 15

ok got that part

Answer 16

Now, you have\[\sqrt{54 x^8}\]yes?

Answer 17

yes

Answer 18

By definition, this is the same as \[\left(54x^8\right)^{\frac{1}{2}}\]and as such will abide by all normal properties of exponents. Such as that we can split them up.\[\left(54\right)^{\frac{1}{2}}\left(x^8\right)^{\frac{1}{2}}\]Of course, this is the same as also saying\[\sqrt{54}\sqrt{x^8}\]

Answer 19

ok

Answer 20

How can we simplify the \[\sqrt{x^8}\]portion?

Answer 21

No idea :) sorry

Answer 22

or \[\left(x^8\right)^{\frac{1}{2}}\]

Answer 23

You have to use the formula I gave you.

Answer 24

ok let see

Answer 25

x^4

Answer 26

I really don't have any idea what I'm doing

Answer 27

Exactly. You can check by squaring it.\[(x^4)^2 = (x\cdot x \cdot x \cdot x)(x\cdot x \cdot x \cdot x)\]\[(x^4)^2=x^8\ \checkmark\]

Answer 28

Oh gosh I'm so confuse

Answer 29

Do you agree that if \[\sqrt a = b\]then\[b^2=a\]?

Answer 30

LOL YOu have no idea how my brain is going around and around

Answer 31

yakey, before you go any further, read what familiapr has posted earlier. he does not understand the concept of squares or square roots. you may be better served by explaining that to him.

Answer 32

Can you break down the problem for me? and explain the process

Answer 33

I explained what a square root is...that's just what I explained before in math symbols. The exact simplification process is as follows. Tell me what step(s) trip(s) you up.\[\sqrt{3x^7}\sqrt{18x}\]\[\sqrt{(3x^7)(18x)}\]\[\sqrt{(3\cdot 18)(x\cdot x^7)}\]\[\sqrt{54x^8}\]\[\sqrt{54}\sqrt{x^8}\]\[\left(54\right)^{1/2}\left(x^8\right)^{1/2}\]\[\left(54\right)^{1/2}x^4\]\[x^4\sqrt{54}\]

Answer 34

You could even go further as follows.\[x^4\sqrt{9\times 6}\]\[x^4 \sqrt 9 \sqrt 6\]\[3x^4 \sqrt 6\]

Answer 35

ok can explain me why x^8 doesn't stay like that?

Answer 36

\[\sqrt{x^8}\]\[(x^8)^{\frac 12}\]\[x^{8\cdot\frac{1}{2}}\]\[x^4\]

Answer 37

I get that , what I'm asking is when you split that x^8 into X^7 and x

Answer 38

I didn't split them...I combined them? They were given separate in the problem, so to simplify you combine them? I was starting from the original problem.

Answer 39

ok

Answer 40

Can you help me with this one? I try and I don't know if is correct I get stuck
\[\sqrt[4]{48x^4y^6}\]