Question

examine whether the following numbers are rational or irrational i) root 7 ii) root 4 iii) 2+ root 3 iv) root 3 +root 2 v) root 5-2 vi) root 23 vii) 1.101001000100001 viii) 7.478478

Answer 1

1. irrational no.
2.rational no.
3. irrational no.
4. irrational no.
5. irrational no.
6. irrational no.
7. irrational no.
8. rational no.
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Answer 2

Answer:

We have to tell if the given numbers are rational or irrational.

Option (i)

√7 is a Irrational no.

Option (ii)

√4 = ± 2

⇒ √4 is rational no.

Option (iii)

2 + √3

√3 is irrational no. and 2 is rational no.

we know that sum of rational and irrational no is a irrational no.

⇒ 2 + √3 is irrational no.

Option (iv)

√3 + √2

√3 is a irrational no. and √2 is a irrational no.

We know that sum of two irrational no is a irrational no.

⇒ √3 + √2 is irrational no.

Option (v)

√5 - 2

√5 is irrational no. and 2 is rational no.

⇒ √5 - 2 is irrational no.

Option (vi)

√23

√23 is a irrational no.

Option (vii)

1.101001000100001... is a non terminating non repeating decimal expansion

⇒ 1.101001000100001...  is irrational no.

Option (viii)

7.478478... is a non terminating repeating decimal expansion.

$7.478478...\,=7.\overline{478}$

⇒ 7.478478... is rational No.