You can
put this solution on YOUR website!When trying to simplify or expand complicated expressions involving roots, you can try substitutions to get the expression into a cleaner form (it's not required, but I find that it helps you see the big picture).
So if we let
and
, we can simplify
to get
(note: I just replaced every
with "x" and every
with "y")
---------------------------------------------------
Now let's FOIL
Remember, when you FOIL an expression, you follow this procedure:
Multiply the
First terms:
.
Multiply the
Outer terms:
.
Multiply the
Inner terms:
.
Multiply the
Last terms:
.
---------------------------------------------------
Now collect every term to make a single expression.
Now combine like terms.
So
FOILs to
.
In other words,
.
---------------------------------------------------------
Start with the last equation
Plug in
(ie replace every "x" with
)
Plug in
(ie replace every "y" with
)
Simplify
Square
to get
(note: the square undoes the square root)
Square
to get
(note: the square undoes the square root)
Combine like terms.
=====================================================================
Answer:
So
You can
put this solution on YOUR website!If you remember, when you are multiplying two binomials, you can use a mind trick called FOIL (first, outside, inside, last). Just in case you haven't heard this before, it means multiply the two first terms of each binomial, then the two outside terms, then the two inside terms, and finally, the two last terms. So, for
So, once we FOIL, we get
Now, simplifying (remember that sqrt(x)sqrt(x)=x) we get
So, oddly enough, that entire expression simplifies to just 1. Doesn't that just annoy you? :)
You can
put this solution on YOUR website!Simplify. Assume that each radical represents a real number.
(√(n+1) +√n)( √(n+1) -√n)
-----------------
Treat the radicals as x and y, then it's (x+y)*(x-y) = x^2-y^2
So it's
(n+1) - n
= 1
(
