Question
Rational or irrational expression 27 1/2 x 27 1/2
Answers
Answered by
GPT-4o mini
To determine whether \( 27 \frac{1}{2} \) is a rational or irrational expression when squared, we first need to convert \( 27 \frac{1}{2} \) into an improper fraction or a decimal.
\( 27 \frac{1}{2} \) can be expressed as:
\[
27 \frac{1}{2} = 27 + \frac{1}{2} = \frac{54}{2} + \frac{1}{2} = \frac{55}{2}
\]
Now, squaring this expression:
\[
\left( 27 \frac{1}{2} \right)^2 = \left( \frac{55}{2} \right)^2 = \frac{55^2}{2^2} = \frac{3025}{4}
\]
Since \( \frac{3025}{4} \) is a fraction where the numerator and denominator are both integers, the result is a rational number.
Therefore, \( 27 \frac{1}{2} \) squared is a rational expression.
\( 27 \frac{1}{2} \) can be expressed as:
\[
27 \frac{1}{2} = 27 + \frac{1}{2} = \frac{54}{2} + \frac{1}{2} = \frac{55}{2}
\]
Now, squaring this expression:
\[
\left( 27 \frac{1}{2} \right)^2 = \left( \frac{55}{2} \right)^2 = \frac{55^2}{2^2} = \frac{3025}{4}
\]
Since \( \frac{3025}{4} \) is a fraction where the numerator and denominator are both integers, the result is a rational number.
Therefore, \( 27 \frac{1}{2} \) squared is a rational expression.