Question

Simplify
square root of 200xyz^3

Answer 1

Hello

Answer 2

An expression containing a square root is considered to be as simple as possible when the
expression inside the square root is as simple or small as possible. The reduction of the contents
inside the square root is accomplished (when possible) by a very straightforward strategy:
(i) Factor the expression inside the square root completely. Write factors which are perfect
squares as explicit squares.
(ii) Use the property that the square root of a product is equal to the product of the square roots
of the factors to rewrite the square root from step (i) as a product of square roots of factors which
are perfect squares and a single square root of an expression which contains no perfect square
factors. The pattern is:
u v w u v w i i⋯ i i i⋯ i =
where u, v, etc. are perfect squares, and w is an expression containing no perfect square factors.
(This may seem a bit abstract, but the meaning of this pattern should become more obvious after
you have studied a few of the examples below. It is important in mathematics not only to study
specific examples of a type of operation, but to eventually understand an overall general strategy
or pattern for similar types of problems.)
(iii) Replace the square roots of perfect squares by factors which are not square roots using the
property
2
u u =
We now illustrate this general strategy with a series of specific examples.
Example 1: Simplify 13 50x .
solution:
The expression inside the square root is nearly completely factored already, but we do need to
write it so that perfect square factors show up more explicitly to complete step (i) in applying the
general strategy given above. We have
50 = 2•5•5 = 2•5
2
and
x13 = x12
•x = (x6
)
2
•x
Thus our original square root can be rewritten as

Answer 3

Sorry I still don't understand!

Answer 4

There are no perfect squares in my problem

Answer 5

\[\sqrt{200}\] isnt a perfect square