Question

how do you solve
(2 squareroot 2 - squareroot 3) ^2
can someone please walk me through how to do it im so confused

Answer 1

Foil it out.
\[(2\sqrt{2} - \sqrt{3})^2 \]\[= (2\sqrt{2} - \sqrt{3})(2\sqrt{2} - \sqrt{3})\]\[=2\sqrt{2}(2\sqrt{2} - \sqrt{3}) - \sqrt{3}(2\sqrt{2} - \sqrt{3})\]\[=...\]

Answer 2

foil...
4sqrt{2} - 4sqrt{6} - sqrt{9}

Answer 3

The first term should be 4sqrt{4} actually.

Answer 4

ya sorry

Answer 5

i know the answer is 11 - 4 squareroot 6 but i was wonderin how to get it...any ideas?

Answer 6

oops ya, i need to watch my signs

neg * neg is a pos

Answer 7

so you should get...
8 - 4sqrt{6} + 3

or

11 - 4sqrt{6}

Answer 8

sorry

Answer 9

use the formula\[ (a-b)^2 = (a^2 - 2ab + b^2)\] there is also a formula for (a+b)^2:\[ (a+b)^2 = (a^2 + 2ab + b^2)\]

Answer 10

wait i dont get it

Answer 11

wait i dont get it

Answer 12

let a = 2sqrt(2) and let b = sqrt(3)

Answer 13

then what kanade?

Answer 14

using the first equation just square 'a'
then multiply '2ab' together and subtract from 'a^2' from previous
then add 'b' squared

Answer 15

by first equation i mean\[ (a−b)^2=(a^2−2ab+b^2)\]

Answer 16

can you try the problem telling me wut u get so i can make sure im doing it right... and i dont get wut u mean by first equation either...

Answer 17

\[(a−b)^2=(a^2−2ab+b^2)\]is what i mean by the first equation, so you have\[ (2 \sqrt2 - \sqrt{3}) ^2 \]Let\[ a = 2 \sqrt2\] and let \[ b = \sqrt{3}\]then plugging in to the equation: \[(a−b)^2=(a^2−2ab+b^2)\]
you get \[(2 \sqrt2−b)^2=((2 \sqrt2)^2−2(2 \sqrt2)(\sqrt{3})+(\sqrt{3})^2)\]

Answer 18

o whoops that b is suppose to be \[\sqrt{3}\] on that last line

Answer 19

then if you simplify that then you should get your answer

Answer 20

so then you should get \[8 - 4\sqrt6 + 3\] through simplification which is \[11-4\sqrt(6)\]

Answer 21

the 8 comes from the \[(2\sqrt2)^2\]
the -4sqrt(6) comes from the \[-2(2\sqrt2)(\sqrt3)\]
the 3 comes from the \[\sqrt3^2\]

Answer 22

what do you mean by through simplification, how do you ghe final answer?

Answer 23

from \[8−4\sqrt6+3 \]to \[11−4(\sqrt6)\]?

Answer 24

if you just solve \[(2\sqrt2)^2−2(2\sqrt2)(\sqrt3)+(\sqrt3)^2)\]

Answer 25

when i meant to simlify i just mean combine like terms, or terms that are similar such as the part where it contains 8 + 3 can be better of written as 11

Answer 26

ok got it now thx