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Prime Divisibility

Class 10 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIn the irrationality proof of (\sqrt{3}), which reasoning is strongest while writing (3\mid p) from (3\mid p^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Expert MathematicsIf (\sqrt{2}=\frac{p}{q}) is assumed in lowest form and (p^2=2q^2) is obtained, what is the most precise reason that (p) is even?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Expert MathematicsWhy is (5\mid b) concluded from (5\mid b^2) in the proof for (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsIf (r) is prime and (r\mid x^2), what conclusion is used in proving the irrationality of (\sqrt{r})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsWhich statement is most essential in proving the irrationality of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Hard MathematicsIf (r) is prime and (r\mid x^2), how is it used in the proofs of (\sqrt{3}) and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Hard MathematicsAssume (\sqrt{3}) is rational and write (\sqrt{3}=\frac{p}{q}). What is the correct reasoning about (p) from (p^2=3q^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Hard MathematicsIf (r) is prime and (r\mid x^2), what is its correct use in the proofs of (\sqrt{3}) and (\sqrt{5})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Hard MathematicsIn the proof of (\sqrt{3}), what is the proper basis for writing (p=3k) from (p^2=3q^2)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Hard MathematicsIf (r) is prime and divides the square (x^2) of an integer (x), what is the correct conclusion?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Medium MathematicsWhile proving the irrationality of (\sqrt{3}), (p^2=3q^2) is obtained. Which conclusion about (p) with reason is correct?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Medium MathematicsIf (r) is prime and (r\mid x^2), which rule is used in irrationality proofs?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Medium MathematicsIf assuming (\sqrt{5}=\frac{m}{n}) and squaring gives (m^2=5n^2), what is the correct next form for (m)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Medium MathematicsIn the proof of (\sqrt{3}), if (q^2=3k^2), what is the correct conclusion about (q)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Easy MathematicsIf (p^2) is divisible by (5), what conclusion is taken about (p)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 18Easy MathematicsIf (a^2=3b^2), what conclusion about (a) is taken in the proof of (\sqrt{3})?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 17Easy MathematicsIf (p^2) is divisible by (5), what is true about (p)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Easy MathematicsIf (p^2) is divisible by (3), what is true about (p)?Class 10Real NumbersProof of irrationality of √2, √3, √5Level 16Easy