Rationalizing the Denominator: 3 - √2/3 + √2
In this article, we will discuss how to rationalize the denominator of the expression 3 - √2/3 + √2.
What is Rationalizing the Denominator?
Rationalizing the denominator is a process in mathematics that involves eliminating radicals or irrational numbers from the denominator of a fraction. This is done to simplify the expression and make it easier to work with.
The Expression: 3 - √2/3 + √2
The given expression is:
3 - √2/3 + √2
To rationalize the denominator, we need to get rid of the square root in the denominator.
Step 1: Multiply the Fraction by the Conjugate
The conjugate of the denominator is obtained by changing the sign of the radical. In this case, the conjugate of the denominator is:
3 + √2
We multiply the fraction by the conjugate:
(3 - √2/3 + √2) × (3 + √2/3 + √2)
Step 2: Simplify the Expression
Expanding the product, we get:
(9 - 2)/3 + √2(3 - 1)
= (7)/3 + 2√2
Step 3: Simplify Further
Combining like terms, we get:
7/3 + 2√2
The Final Answer
The rationalized form of the expression 3 - √2/3 + √2 is:
7/3 + 2√2
In this article, we have successfully rationalized the denominator of the given expression using the conjugate method.
