Question

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Answer 1

(2sqrt(5) +3sqrt(7))^2 = (2sqrt(5) +3sqrt(7))(2sqrt(5) +3sqrt(7))

= 2sqrt(5)2sqrt(5) + 2sqrt(5)3sqrt(7) + 3sqrt(7)2sqrt(5) + 3sqrt(7)3sqrt(7)

= 20 + 6sqrt(5)sqrt(7) + 6sqrt(7)sqrt(5) + 63

= 83 + 12sqrt(5)sqrt(7)

Answer 2

i don't undertsand is there a simlyer way to do it?

Answer 3

\[(a+b)^2=a^2+2ab+b^2\]
use this
here
\[a=2\sqrt{5}\]\[b=3\sqrt{7}\]

Answer 4

not really. perhaps if i use the equation writer it will be clearer:

\[(2\sqrt{5} +3\sqrt{7})^2 = (2\sqrt5 +3\sqrt7)(2\sqrt5+3\sqrt7)\]
\[=2\sqrt5(2\sqrt5 + 3\sqrt7) + 3\sqrt7(2\sqrt5 + 3\sqrt7)\]
\[= (2\sqrt5)(2\sqrt5) + (2\sqrt5)(3\sqrt7) + (3\sqrt7)(2\sqrt5) + (3\sqrt7)(3\sqrt7)\]

\[=4(\sqrt5)^2 + (2\sqrt5)(3\sqrt7) + (2\sqrt5)(3\sqrt7)+ 9(\sqrt7)^2\]

Answer 5

ok ok thank u

Answer 6

I got something different. Tell me where i went wrong. Check the attached file(my solution).

Answer 7

\[\large (2\sqrt{5}+3\sqrt{7})^2 \neq (2\sqrt{5})^2+ (3\sqrt{7})^2\]

Answer 8

\[(a+b)^2= a^2+2ab+b^2\]

Since:\[(a+b)^2=(a+b)(a+b)\]\[a(a+b)+b(a+b)\]\[a^2+ab+ba+b^2\]\[a^2+2ab+b^2\]

Answer 9

Thanks alot. I see my mistake now. I really appreciate your assistance.

Answer 10

you're Welcome :)