Is the simplified form of 2 square root of 3 + 3 square root of 3 rational?
yes or no i think its yes pls help
2√3 + 3√3
= 5√3 which is still irrational
thx so much
To determine if the simplified form of the expression 2√3 + 3√3 is rational, let's break it down step by step.
First, we can combine the terms with the same radical, which in this case is √3. The two terms are 2√3 and 3√3. Adding them together, we get:
2√3 + 3√3 = (2 + 3)√3 = 5√3
Now, to determine if 5√3 is rational, we need to understand the definition of a rational number. A rational number is any number that can be expressed as a fraction, where both the numerator and the denominator are integers.
However, 5√3 cannot be expressed as a fraction because the square root of 3 is an irrational number. It means that it cannot be written exactly as a fraction or a terminating decimal. As a result, 5√3 is an irrational number.
Therefore, the simplified form 2√3 + 3√3 is not rational.