Simplify.

Question

Simplify.

anonymous · Answer

$$3\sqrt{5}-2\sqrt{7}+\sqrt{45}-\sqrt{28}$$

e.mccormick · Answer

K.  Any idea on where to start this sort of problem?

anonymous · Answer

@dumbcow @happyrosy @Marina17

e.mccormick · Answer

In a way, radicals work like fractions.  With a fraction, they can only be added or subtracted if the same thing is on the bottom but they can always be multiplied.  With a radical the same rule apples in that they can only be added or subtracted if the same thing is under the radical but they can always be multiplied.

So start by seeing if you can get the same thing under the radical for the 45 and 28 as the 5 or 7.

dumbcow · Answer

you have to combine like terms

start by simplifying radicals

example:
sqrt(12) = sqrt(4)*sqrt(3) = 2*sqrt(3)

anonymous · Answer

$$\sqrt{12} = \sqrt{4}\sqrt{3} =\sqrt{3}$$ like that?

dumbcow · Answer

yes

anonymous · Answer

with a 2 infront of the sqrt 3

anonymous · Answer

and after that?

e.mccormick · Answer

Another example of the type of thing they want you to do:

$\sqrt{12}+\sqrt{3}\implies $

$\sqrt{3\cdot 4}+\sqrt{3}\implies $

$2\sqrt{3}+\sqrt{3}\implies $

$3\sqrt{3} $

dumbcow · Answer

well simplify sqrt(45) , what perfect square is a factor of 45

anonymous · Answer

$$3\sqrt{5}$$ ?

anonymous · Answer

is that wrong?

dumbcow · Answer

yes that is correct

dumbcow · Answer

now the 28?

anonymous · Answer

the answer choices are:
$$2\sqrt{12}       $$
$$2\sqrt{2}$$
$$6\sqrt{5}-4\sqrt{7}$$
$$6\sqrt{10}-4\sqrt{14}$$

anonymous · Answer

5 for the 28

dumbcow · Answer

haha , we'll get there
first simplify sqrt28

anonymous · Answer

5

dumbcow · Answer

nope, what are factors of 28?

anonymous · Answer

$$3 \sqrt{5}-2 \sqrt{7}+\sqrt{45}-\sqrt{28} $$$$3 \sqrt{5}-2 \sqrt{7}+3 \sqrt{5}-2 \sqrt{7} $$$$6 \sqrt{5}-4 \sqrt{7} $$

e.mccormick · Answer

Answer choices don't really matter.  If you know the process, you can get the answer.  Then you will see the proper choice in the end.  =)

dumbcow · Answer

just like
45 = 9*5

anonymous · Answer

sorry, I thought it was 25 instead of 28 XD

anonymous · Answer

so I just continue the process til I can't simplify anymore?

dumbcow · Answer

yes then add like radicals as shown by @e.mccormick example and @robtobey

anonymous · Answer

okay thanks, you guys were a big help c:

dumbcow · Answer

yw:)