Question

I need help I'm not so should what I'm supposed to do
Simplify the radical expression. Assume that all variables represent positive real numbers

Answer 1

\[5\sqrt{75d ^{2}x}+7d \sqrt{12x}\]

Answer 2

Begin by simplifying each term. The largest square factor of the radicand in the first term.
\[\sqrt{75}=15\times5\]
\[\sqrt{12}=3\times4\]

Answer 3

@ScarlettFarra2000 so yeah just another thing try to look to see if there are any perfect squares, that are factors of the number you're interested in. let's take your other example for instance .

this is what you had here

\[\sqrt{12} = \sqrt{4}*\sqrt{3} = 7d*2\sqrt{3}\]

Answer 4

now perfect squares could be 25, 16,4,36, etc

Answer 5

let's take a look at \[\sqrt{75}\] we know that 75 is divisible by 25 right?

because

\[25*3 = 75\]

now check this out

it's the same if we put a square root on all of them

\[\sqrt{25}*\sqrt{3} =\sqrt{75}\]

Answer 6

Okay, so that's the first step right?

Answer 7

what do you notice about radical 25?

Answer 8

It can b e simplify be 5

Answer 9

so this is the point @ScarlettFarra2000 we need to find a perfect square that is a factor of our number

Answer 10

so take a look at this again

\[\sqrt{75} = \sqrt{25}*\sqrt{3} = 5\sqrt{3}\]

Answer 11

\[5*5\sqrt{3d^{2}x}\]

now take a look at that d^2x

we can take out a d because the square root of d^2 is just d

so it becomes

\[25d \sqrt{3x}\]

Answer 12

now based on what I did for the first term, how would we simplify the second term?

Answer 13

As we look at \[\sqrt{12}\]\[\sqrt{6}\times \sqrt{2}=\sqrt{12}?\]

Answer 14

one of those numbers has to be a perfect square

Answer 15

@ScarlettFarra2000

Answer 16

yes?

Answer 17

Can you see why it would be this?

\[\sqrt{4}*\sqrt{3} = \sqrt{12}\]

Answer 18

what do you notice here that's different from the answer you just gave?

Answer 19

Is it because you can make 4 smaller?

Answer 20

it's because you can simplify 4 to 2 easily

Answer 21

what do you think @robtobey?

Answer 22

@ScarlettFarra2000 what part are you having trouble with?

Answer 23

I'm still not getting it I understand it some like I know how you did some of it like \[25\times5=75 \] and \[3\times4=12\] and I Know why you used those numbers but is that it or is there more to this problem? Or am I over thinking it?

Answer 24

Given:\[5\sqrt{75d ^{2}x}+7d \sqrt{12x},\]Look for the perfect square factor or factors under each of the radical signs:

Answer 25

\[5\sqrt{75d ^{2}x}+7d \sqrt{12x}=5\sqrt{3*25d ^{2}x}+7d \sqrt{3*4x}\]

Answer 26

A factor common to both of the two terms on the right is Sqrt(3x). This can't be simplified further, but the rest of the expression can. Try it.

Answer 27

If you have a smartphone, to check your answers download photomath, and type it in and it shows you all the steps.

Answer 28

Thanks @mathmale the answer \[39d \sqrt{3}\]

Answer 29

Happy to be of help. Photon did a great job of helping also, I thought.

Answer 30

He did I'm just not so great at math

Answer 31

\[39 d \sqrt{3 x} \]Refer to the attached solution from the Mathematica program.

Answer 32

Thank you @robtobey but I got the answer wrong last time and ever time it's wrong it resets the problem it's almost impossible ever finish this assignment

Answer 33

Scarlett: It's really, really important that you study this conversation, so that next time you try to work a problem of this kind, you know the proper steps to take. As before, you need to identify any perfect squares that you spot under each radical sign. THAT is the key to simplifying these expressions.

Answer 34

Okay it's just I'm having a REALLY hard time with this lesson some parts I get others not so much