Let p, q and r be three distinct prime numbers. Check whether p · q · r + q is a composite number or not. Further, give an example for 3 distinct primes p, q, r such that

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CASE_STUDIESPrime Factorisation of Natural NumbersIrrationality of Square Root of Prime NumbersCBSE PYQ2 sub-questions

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Prove that 5 − 2√3 is an irrational number. It is given that √3 is an irrational number.

Show that the number 5×11×17+3×11 is a composite number.

TextPrime Factorisation of Natural NumbersIrrationality of Square Root of Prime NumbersProof by Contradiction Method

Which of the following cannot be the unit digit of 8ⁿ, where n is a natural number ?

Prove that √5 is an irrational number.

Prove that √3 is an irrational number.

State true or false for each of the following statements and justify in each case :