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Prove that √3 is an irrational number.
State true or false for each of the following statements and justify in each case :
If x = ab³ and y = a³b, where a and b are prime numbers, then [HCF (x, y) – LCM (x, y)] is equal to :
Prove that √2 is an irrational number.
Let x and y be two distinct prime numbers and p = x²y³, q = xy⁴, r = x⁵y². Find the HCF and LCM of p, q and r. Further check if HCF (p, q, r) × LCM (p, q, r) = p × q × r or not.
The HCF of 40, 110 and 360 is :
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