Is \(\frac{36}{81}\) a perfect square?
Answer (3)
Y ES b ec a u se 36 = 6 2 81 = 9 2 t h ere f ore 81 36 = ( 9 6 ) 2
The fraction 36/81 is a perfect square because, after simplification, it results in 4/9, where both 4 and 9 are perfect squares (2² and 3² respectively).
To check if 36/81 is a perfect square, we need to simplify the fraction and see if the numerator and the denominator are both perfect squares. Simplifying 36/81, we get 4/9 since both 36 and 81 are divisible by 9. Now, 4 is a perfect square as it is 2 squared (2²), and 9 is a perfect square as it is 3 squared (3²). Therefore, the simplified fraction is the division of two perfect squares, which makes 36/81 a perfect square.
The fraction 81 36 can be expressed as ( 3 2 ) 2 , indicating that it is a perfect square. Thus, the answer is yes, it is a perfect square.
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