Question

plzz answer

its urgent

1) prove that √13+√17 is an irrational number. (2)can two numbers have 18 as their HCF and 380 as their LCM. give reason.

Answer 1

Please refer to the first chapter of class 10 ncert book.
The proof is a little long but it's easy.

The second one can be possible only if the hcf is a factor of the lcm.

Answer 2

No. The highest common factor (HCF) by definition divides both numbers, and both numbers by definition divide the lowest common multiple (LCM), so we will always find that the HCF of a set of numbers divides their LCM.

18 does not divide 380 (380÷18=2119380÷18=2119) so these cannot be the HCF and LCM of two numbers.