Simplifying the Algebraic Expression: 14/3 - √2
In this article, we will discuss how to simplify the algebraic expression 14/3 - √2. This expression involves a combination of rational numbers and irrational numbers, making it a bit challenging to simplify.
Rationalizing the Denominator
To start, let's focus on the fraction part of the expression, which is 14/3. To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 14 and 3 is 1, so we can simplify the fraction as follows:
14/3 = 4 2/3
Now, let's move on to the irrational part of the expression, which is -√2.
Simplifying the Irrational Part
The expression -√2 cannot be simplified further since it is already in its simplest form. However, we can try to rationalize the denominator by multiplying the numerator and denominator by √2.
-√2 = (-√2) / 1 = (-√2) / 1 * (√2 / √2) = -2 / √2
Now, let's combine the rational and irrational parts of the expression.
Final Simplification
Combining the simplified rational and irrational parts, we get:
14/3 - √2 = 4 2/3 - 2 / √2
This is the simplified form of the original expression. Note that we cannot simplify the expression further since it involves a combination of rational and irrational numbers.
In conclusion, we have successfully simplified the algebraic expression 14/3 - √2 by rationalizing the denominator and combining the rational and irrational parts.
