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(9) Give an example of two irrational numbers such that the product is a rational number.

Ask by Savage Matthews. in Malaysia
Jan 20,2025

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An example of two irrational numbers whose product is rational is \( \sqrt{2} \) and \( \sqrt{2} \), since \( \sqrt{2} \times \sqrt{2} = 2 \).

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The Deep Dive

Consider the irrational numbers √2 and √8. When you multiply them together, you get: √2 * √8 = √(2 * 8) = √16 = 4, which is a rational number! This nifty little trick showcases how sometimes, mixing certain irrational numbers can cook up a rational result. Who knew math could be so delightfully puzzling? Another example is taking the irrational number π (pi) and its counterpart 0. Adding the twist of a fraction, you could look at (π) and (1/π). Their product would be: π * (1/π) = 1, which, you guessed it, is a rational number. It's like cooking up a perfect mathematical meal where everything adds up just right!

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