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Which 3 of the following numbers are irrational?

PLEASE ONLY ANSWER IF YOU KNOW THE ANSWER.


13 + √(25)

17\pi

.21475467...

\sqrt{ (9 )/(16) }

- (4)/(5) + \sqrt{ (6)/(9) }




User Laanwj
by
6.7k points

1 Answer

5 votes

Answer:

The irrational numbers from the given options are :-


  • 17\pi

  • 0.21475467.....

  • -(4)/(5) + \sqrt{(6)/(9) }

Explanation:

Analyse each option carefully.

1)
13 + √(25) is a rational number because :-


  • √(25) = 5

  • 13 + √(25) = 13 + 5 = 18 , which is a rational number.

2)
17\pi is irrational because :-

  • Value of π has a non-terminating & non-recurring decimal value. So it is irrational number.
  • If π is irrational , then 17π is also irrational because product of any number and an irrational number is always irrational.

3)
0.21475467.... is irrational because :-

  • It is a non-terminating & non-recurring decimal.
  • Any non terminating & non-recurring decimal is an irrational number.

4)
\sqrt{(9)/(16) } is rational because :-


  • \sqrt{(9)/(16) } = (√(9) )/(√(16) ) = (3)/(4).

  • (3)/(4) is a rational number.

5)
-(4)/(5) + \sqrt{(6)/(9) } is irrational because :-


  • \sqrt{(6)/(9) } = (√(6) )/(√(9) ) = (√(6) )/(3) , which is irrational.
  • If
    (√(6) )/(3) is irrational , then
    -(4)/(5) + \sqrt{(6)/(9) } is also irrational because sum of any number and an irrational number is always an irrational number.
User ElMarquis
by
6.5k points
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