Home › UP Board Class 10 › Mathematics › Real Numbers › If p is prime and p divides a², then p divides a…
If p is prime and p divides a², then p divides a. This step is used to prove which number irrational in NCERT?
A√2
B0.5
C22/7
Dπ
Answer & Solution
Correct answer: A. √2
The "p | a² ⇒ p | a" lemma is the linchpin of the contradiction proof that √2 is irrational. The same template handles √3 and √5.
Related questions
The largest number that divides both 60 and 96 exactly (their HCF) isThe decimal expansion of an irrational number isThe sum of a rational number and an irrational number is alwaysThe product of the HCF and LCM of the numbers 8 and 20 isA rational number $\dfrac{p}{q}$ (in lowest terms) has a terminating decimal expansion if The prime factorisation of 140 isUsing Euclid's algorithm, the HCF of 96 and 404 isIf the HCF of two numbers is 9 and their LCM is 90, and one number is 18, the other number