Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form of
is
.
Solution
To rationalize the denominator of the expression
and simplify it, follow these steps:
-
Multiply by
over itself: -
Simplify the denominator:So, the expression becomes:
-
Cancel out the common factor of 2 in the numerator and the denominator:
Therefore, the rationalized and simplified form of
is:
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg


Beyond the Answer
To rationalize the denominator of
, multiply both the numerator and the denominator by
:
Now, simplify the fraction:
So,
simplifies to
.
Rationalizing the denominator is a clever trick that helps avoid messy calculations or interpretations, especially in fields like engineering where precise measurements are vital. It ensures expressions are in a more standard form, making them easier to work with and compare.
When working on problems like this, a common mistake is to forget to multiply both the top and bottom by the same number, which can lead to incorrect results. Always remember to keep the fraction equivalent!