Math, asked by Vishalagnii4684, 8 months ago

Which of following is not irrational? (3+√7) (3-√7) (3+√7) (3-√7) (3√7)

Answers

Answered by RvChaudharY50
26

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.

_________________________

Extra :-

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

__________________________

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

Answered by piyush9451d
6

Answer:

option 3

Step-by-step explanation:

(3+√7) (3-√7)

hope it will help you

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