SOLUTION: Write in simplified form the square root of 5/the square root of 2b

Algebra ->  Radicals -> SOLUTION: Write in simplified form the square root of 5/the square root of 2b      Log On


   

Question 72254This question is from textbook Elementary Algebra
: Write in simplified form
the square root of 5/the square root of 2b This question is from textbook Elementary Algebra

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
The problem is to simplify:
.
sqrt%285%29 divided by sqrt%282%2Ab%29
.
Let's first show the division of these two terms:
.
%28sqrt%285%29%29%2F%28sqrt%282%2Ab%29%29
.
But it is normally considered bad form to leave a radical in the denominator. Therefore,
let's multiply this entire expression by %28sqrt%282%2Ab%29%29%2F%28sqrt%282%2Ab%29%29.
.
You may notice that this multiplier equals 1 because the numerator and denominator are identical.
So by multiplying this times the original problem we are just multiplying the problem
by an expression that equals 1.
.
This gives us:
.

.
which combines to:
.
%28sqrt%285%29%2Asqrt%282%2Ab%29%29%2F%28sqrt%282%2Ab%29%2Asqrt%282%2Ab%29%29
.
The product in the denominator is sqrt%282%2Ab%29%2Asqrt%282%2Ab%29 and it equals 2%2Ab.
So the expression becomes:
.
%28sqrt%285%29%2Asqrt%282%2Ab%29%29%2F%282%2Ab%29
.
But by the rules of radical operations the product of the two terms in the numerator
can be combined under a single radical sign to give:
.
sqrt%285%2A2%2Ab%29%2F%282%2Ab%29
.
and finally multiply the two terms inside the radical sign to get:
.
sqrt%2810%2Ab%29%2F%282%2Ab%29
.
This is an acceptable answer, but if you prefer, you can also write it as:
.
%281%2F%282%2Ab%29%29%2Asqrt%2810%2Ab%29
.
Hope this helps you to understand the processes involved in messing around with radicals.