Square root problem with addition?

Question

I don't understand how to do this problem:

(13+sqrt(5)) * (13-sqrt(5))


My calculator says that the answer is 164 but I don't understand how it got that. Help please.

Thanks for all of the help. I understand now.

Answer 1

(13)^2-(sq.rt.5)^2
like (a+b)(a-b)=a^2-b^2
169-5=164

Answer 2

This can be solved using Algebra.

Assume: a = 13, and b = sqrt(5)

Therefore, you get (a + b)*(a - b) where you break down and multiply the first unit (a + b) to a, and (a + b) to b. (Distributivity)
which is = a (a + b) - b (a + b)
= a.squared + ab - ab - b.squared
where ab - ab = 0, therefore
= a.squared - b.squared
Substituting a = 13, and b = sqrt(5)
you get
= 13.squared - (sqrt(5)).squared
where 13.squared = 169 and (sqrt(5)).squared = 5
= 169 - 5
= 164

So, your calculator is correct. ;)

Got it? Good.

Answer 3

Do the FOIL method (First Outside Inside Last)

1. 13 * 13 = 169 Plus the Ouside
2. 13 * (-sqrt(5)) = - 13sqrt(5) Plus inside
3. sqrt(5) * 13 = 13sqrt(5) plus last
4. sqrt(5) * (-sqrt(5)) = -5

steps 2 and 3 cancel each other out, you are left with 169 -5 which equals 164.

Answer 4

you should have been taught how to do this problem in your pre-algebra class.... nonetheless, it's been a while for me, i belieive it is done using F(first) O (outside) I (inside) L (last).
F 13*13
O 13*(-sqrt(5))
I sqrt(5)*13
L sqrt(5)*(-sqrt(5))

Add all the answers together and that should give you the finished product. good luck and don't ever forget about FOIL.

Answer 5

the square root of 5 = 2.24(rounded)
SO I took 13 plus 2.24 and came up with 15.24
and then took 13 minus 2.24 and came up with 10.76
then multiplied 15.24 times 10.76 and came up with 164(rounded)
Did that help? or not?

Answer 6

Multiply them together just you would something that looks like (13-x)*(5-x) treat the square roots like the x's. sqroot of 5 times sqroot of 5 = sqroot of 5 SQUARED. when you have a square root that is squared, it is just he number. 5. then complete the problem using simple math.