Simplifying Radicals:
2�ã108
-----
�ã180y
The check mark represents the radicand. How do I work this problem?
Sorry, the radicand came out in a code.
It is 2(radicand)108 over
(radican)180y
2√108/√(180y)
= 2√36 √3 / )√36 √5y)
= 2√3/√(5y)
or rationalized ....
= 2√(15y)/(5y)
To simplify the given expression, first, let's simplify the radicands (the numbers inside the square roots).
Step 1: Simplify the radicands inside the numerator and denominator:
For the radicand 108, we can break it down into its prime factors: 2 * 2 * 3 * 3 * 3.
For the radicand 180, we can break it down into its prime factors: 2 * 2 * 3 * 3 * 5.
Step 2: Simplify further by taking out any common factors from the numerator and denominator:
In this case, we can see that both radicands share two 2's and two 3's as common factors. We can take them out from under the square roots:
2 * 2 * �ã(3 * 3) 2 * 3 * �ã(2 * 3)
The simplified expression becomes:
2 * 3 * �ã(2 * 3)
--------------
�ã180y
Step 3: Continue simplifying the expression:
We can also simplify the √(2 * 3) inside the square root to get √6. Therefore, the expression becomes:
2 * 3 * �ã6
-----------
�ã180y
Step 4: Simplify the expression further if possible:
In this case, there are no more common factors between the numerator and the denominator. So, the simplest form of the expression is:
6�ã6
-------
�ã180y
Therefore, the simplified expression is 6�ã6/�ã180y.