- Flashback of IX real Number's
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- Euclid's Division Lemma
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- Proof of Euclid's Division Lemma
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- HCF (Highest common factor)
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- What is Prime Numbers
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- What is Composite Numbers
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- Fundamental Theorom of Arithmetic
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- HCF and LCM by prime factorization method
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- Irrational Numbers
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- How to prove the irrational numbers or Rational numbers

- Real number problem and Solutions
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- Real number Worksheet
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- Real number problems
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- Real number Important questions

1) Find the nature of the product (√2 -√3) ( √3 + √2) ?

2) Prove that the sum of a rational number and an irrational number is always irrational.

3) Prove that √5 is an irrational number.

4) Show that 3 + 5√2 is an irrational number. Is sum of two irrational numbers always an irrational number?

5) Prove that √3 is an irrational number and hence show that 2√3 is also an irrational number.

6) Prove that 5 - √3 is an irrational number.

7) Prove that 2√5 is an irrational number.

8) Show that (√3+ √5)

9) Prove that 4 - √5 is an irrational number.

10) Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.

12) Prove that for any positive integer n, n

13) If n is rational and √m is irrational, then prove that (n + √m) is irrational.

14) Show that one and only one out of n, n + 4, n + 8, n + 12 and n + 16 is divisible by 5, where n is any positive integer

15) Prove that √11 is irrational.

16 Show that 3√2 is irrational.

17) Show that 4

18) The product of a non-zero rational and an irrational number is

(A) always irrational

(B) always rational

(C) rational or irrational

(D) one

19) Prove that √p + √q is irrational, where p, q are primes.

20) Prove that one of any three consecutive positive integers must be divisible by 3.

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