Question :- Which of following is not IRRATIONAL ? {(3+√7) (3-√7)} , or (3√7) ?

Solution :-

Solving First we get,

→ {(3+√7) (3-√7)}

using (a + b)(a - b) = (a² - b²) we get,

→ {(3)² - (√7)²}

Now using , (√a)² = a, we get,

→ (9 - 7)

→ 2

→ (2/1)

→ in the FORM of p/q, where q ≠ 0.

Therefore,

{(3+√7) (3-√7)} is a rational Number.

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Now, Solving second part :-

→ 3√7

→ 3 * √7

→ 3 can be written as (3/1) , where denominator is not ≠ 0 , so a rational number).

→ √7 is a non perfect natural number . As we know that, any non non perfect natural number is always an irrational number).

Therefore,

→ (Rational) * (Irrational)

→ Irrational Number.

Hence, we can conclude that, {(3+√7) (3-√7)} is not an irrational number.

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Extra :-

• Rational + irrational = rrational .
• Rational - irrational = rrational .
• Rational * irrational = rrational .
• Rational ÷ irrational = rrational .

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Note :- { if we assume all parts of questions different, than, all are irrational numbers as TOLD in extra. } .