Question

can someone please help me, I have difficulty understanding math.
for example (2squareroot(5)+2)^2

Answer 1

\[(2\sqrt{5}+2)^2=(2\sqrt{5}+2)(2\sqrt{5}+2)=2\sqrt{5}(2\sqrt{5}+2)+2(2\sqrt{5}+2)\]

Answer 2

Go from there.

Answer 3

Foil would work here.

Answer 4

thanks a bunch the thing is that I dont know how to work with the square roots :(

Answer 5

So...\[\left( 2\sqrt{5} + 2 \right)\left( 2\sqrt{5} + 2 \right) = 2\sqrt{5}(2\sqrt{5}) + 2\sqrt{5}(2) + 2(2\sqrt{5}) + 2(2)\]

Answer 6

well, if you do \[(2\sqrt{5})(2\sqrt{5})\] it's 4*5 because the square roots cancel out because they're squared

Answer 7

It's not different from regular numbers, really.

Take the first term as an example: \[2\sqrt{5}(2\sqrt{5})=4\sqrt{5}\sqrt{5}=4\cdot 5=20\]

Answer 8

The rest of your problem reduces to things you already know, I think.

Answer 9

and \[2(2\sqrt{5}) = 4\sqrt{5}\]

Answer 10

I know i may be asking for much but It's been a long while i haven't gone to school and ive been having a hard time and i really don' understand it

Answer 11

it's like the square root 5 is it's own variable, 2x * 2 = 4x
but if you square it, then it turns into a normal # - 5

Answer 12

Excellent analogy. That is usually how it is explained.

It also has to do with the fact that you can't "simplify" two numbers which do not have the same exponent. For example, \(2\sqrt{2}\) cannot be simplified further.

Answer 13

I appreciate you alls help but i dont get it

Answer 14

Precisely what is confusing you?
Do you see how:
\[(2\sqrt{5}+2)^2=(2\sqrt{5}+2)(2\sqrt{5}+2)\]
?

Answer 15

yes that i do see why its twice because of the exponent 2 and how that becomes 4square root 5 because 2*2=4

Answer 16

what do you not get?

Answer 17

but then it has a +2 and what do i do with that one?

Answer 18

i square it as well?

Answer 19

oh at the end, 2*2 = 4.

Answer 20

you treat 2sqrt(5) and 2 as different #s

Answer 21

Okay, let me work you through it.

Answer 22

the actual problem is (2sqrt(5) +2)^2 so then my final answer would be what? 4sqrt(5)+4?

Answer 23

ok thanks alot

Answer 24

\[(2√5+2)(2√5+2)=2√5(2√5)+2√5(2)+2(2√5)+2(2) = 20 + 4√5 + 4√5 + 4 = 24 + 8√5\]

Answer 25

oh, you can't see all of it. well then you have 20 + 4√5 + 4√5 + 4

you can combine 4√5 and 4√5 to get 8√5
and 20 + 4 = 24

so your final answer should be 24 + 8√5

Answer 26

do you understand how i got that?

Answer 27

no the 20 how did u get it ?

Answer 28

ive got this other one (6-sqrt(3)) (6+sqrtroot(3)

Answer 29

2√5 * 2√5 = 2*2*√5*√5 = 4*√25 = 4*5 = 20

Answer 30

for your other problem, it's called difference of two squares. \[\left( 6 - \sqrt{3} \right)\left( 6 + \sqrt{3}\right) = 36 - 3 = \]

Answer 31

if the two binomials fit this formula: \[\left(a + b \right) \left( a - b \right)\] then the answer is \[a ^{2} - b ^{2}\]

Answer 32

this is because the in-between terms would be -ab + ab, so they cancel out. so your other problem's answer is 36 - 3, or 33.