Question

Simplify ?!
(2+√10)(2-√10)

Answer 1

@thomaster could you help?

Answer 2

@Hero

Answer 3

@jim_thompson5910 could you help

Answer 4

Have you tried anything here so far? Or had any ideas that might work out but you' re unsure of?

Answer 5

@AccessDenied Not really. because 10 isn't a perfect square

Answer 6

When I look at this, I think about a factoring trick: difference of squares? is that one familiar?
\(a^ 2 - b^ 2 = (a + b)(a -b) \)

Answer 7

@AccessDenied yeah i think so..

Answer 8

So the reason I bring that up is, the right side of that equation matches what we have now if we called a = 2 and b = sqrt(10). And on the left side, we end up squaring the 2 and that pesky square root of 10 as well.
Or filling in the details:
\( 2^ 2 - \sqrt{10}^2 = (2 + \sqrt{10})(2 - \sqrt{10}) \)
Can you see how to simplify the left side now? (Square root and square cancel first)

Answer 9

@AccessDenied so then we just cancel out the squaring of 2 and 10 so it would just be
2-√10?

Answer 10

@AccessDenied hello?

Answer 11

You would not change 2^2. The square root on the 10 and the square cancel out each other as they are inverses. Like this:
\( 2^ 2 - \sqrt{10}^2 = 2^2 - 10 \)

Answer 12

@AccessDenied oh okay. so then we would end up with 2^2 - 10?

Answer 13

Well, you can simplify more from there. Order of operations, we do the exponents first: 2^ 2 = 2*2 = 4. Then subtract 4 - 10. Makes sense?

Answer 14

@AccessDenied yes okay. so then the answer would be -6.?

Answer 15

Yes. :)

Answer 16

@AccessDenied yay thank you for your help.:)

Answer 17

You' re welcome!