Question

Simplify (sqrt x + sqrt 3) (sqrt x + sqrt 27)
show work or explain please

Answer 1

Hint: (a+b) (c+d) = ac +ad + bc +bd

Answer 2

do i keep the roots?

Answer 3

yes first keep the roots....
tell me what u got

Answer 4

ok so I got \[\sqrt{x}\sqrt{x}+\sqrt{x}\sqrt{27}+\sqrt{3}\sqrt{x}+\sqrt{3}\sqrt{27}\]

Answer 5

good

Answer 6

Now,

Answer 7

Can u use it too

Answer 8

\[x+\sqrt{27x}+\sqrt{3x}+9\]

Answer 9

or i guess\[x+\sqrt{30x}+9\]

Answer 10

good

Answer 11

Now what??

Answer 12

I figured out the answer is \[x+4\sqrt{3x}+9\] But I do not understand how you get \[4\sqrt{3x}\] from \[\sqrt{27x}+\sqrt{3x}\]

Answer 13

@kirk.freedman \[\sqrt{27x}+\sqrt{3x}\neq \sqrt{30x}\]Therefore your above answer is incorrect. I don't know why @sauravshakya said "good"? I know he knows better than that. Maybe he was tired or rushing.

You can only add or subtract two radicals by adding or subtracting the numbers in front iff they have the same index and the same radicand. You can multiply or divide two radicals by multiplying or dividing their radicands iff they have the same index.

The only thing wrong about your answer is the root 30x. you should simplify the sq.root of 27x first. Like this:\[\sqrt{27x}=\sqrt{9}\sqrt{3x}=3\sqrt{3x}\] Thus\[(\sqrt{x}+\sqrt{3})(\sqrt{x}+\sqrt{27})\]\[=x +\sqrt{27x}+\sqrt{3x}+\sqrt{81}\]\[=x +3\sqrt{3x}+\sqrt{3x}+9\]\[=x +4\sqrt{3x}+9\]And this @kirk.freedman is your final answer!

Answer 14

So if \[\sqrt{27x}= 3\sqrt{3}\] you still have the other \[3\sqrt{3}\] don't you?

Answer 15

I'm sorry, add an x into those above.

Answer 16

No the other one is just root 3. 3 root 3 is only derived from simplifying root 27. Understand?

Answer 17

Well x or no x, 3 root 3 is only derived from simplifying root 27.

Answer 18

oh wait so rt27x= 3rt3x, and still have the rt3x though??

Answer 19

Yes!

Answer 20

from the equation above \[x+\sqrt{27x}+\sqrt{3x}+9\] See we still have the \[\sqrt{3}\]?? do we just get rid of it or what? Because we end up having \[3\sqrt{3x}+\sqrt{3x}\]

Answer 21

Did you not read every single line of my explanation above, because I explained this very clearly.

Answer 22

OHHHHHHHHH I got it, thanks so much!

Answer 23

3 root 3 + 1 root 3 = 4 root 3 because 3 + 1 = 4.

Answer 24

Good, Excellent!

Answer 25

Sorry I was saying good for the first one...
And I was unable to continue as my internet stop working