Which of following is not irrational? (3+√7) (3-√7) (3+√7) (3-√7) (3√7)
Answers
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. } .
Answer:
option 3
Step-by-step explanation:
(3+√7) (3-√7)
hope it will help you