Rationalizing the Denominator: Simplifying 12/√3
In mathematics, rationalizing the denominator is a process of eliminating irrational numbers from the denominator of a fraction. In this article, we will explore how to simplify the fraction 12/√3.
What is 12/√3?
The fraction 12/√3 is a mathematical expression that consists of a numerator (12) and a denominator (√3). The denominator is an irrational number, which makes the fraction difficult to work with.
Rationalizing the Denominator
To rationalize the denominator, we need to eliminate the irrational number √3 from the denominator. We can do this by multiplying both the numerator and the denominator by √3.
Step 1: Multiply by √3
Multiply both the numerator and the denominator by √3:
(12/√3) × (√3/√3) = 12√3 / (√3)²
Step 2: Simplify the Denominator
Simplify the denominator by evaluating (√3)²:
(√3)² = 3
So, the expression becomes:
12√3 / 3
Step 3: Simplify the Fraction
Simplify the fraction by dividing both the numerator and the denominator by 3:
12√3 / 3 = 4√3
And that's it! We have successfully rationalized the denominator and simplified the fraction 12/√3 to 4√3.
Conclusion
In conclusion, rationalizing the denominator is an important skill in mathematics that helps us to simplify fractions with irrational numbers in the denominator. By following the steps outlined above, we can simplify complex fractions like 12/√3 and make them easier to work with.
