Prove that if p is a prime, then the square root of p is irrational.

Q: Prove the following using the specified technique: (a) Prove by contrapositive that for any two real…

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Q: Find two irrational numbers a and b such that a is rational.

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Q: Prove that if a and b are positive integers and ab is not a square, then √a + √b is irrational

A: Given a & b are positive integer and ab is not perfect square. We have to prove that √a+√b is…

Q: ▷ Prove that √2 + √3 is irrational.

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Q: Prove the following statement whether is true or false:For any two non-zero real numbers,if their…

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Q: 3. Prove that √12 is irrational using the Fundamental Theorem of Arithmetic.

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Q: Show that these statements about the real number x are equivalent: (i) x is irrational, (ii) 3x + 2…

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Q: Suppose p and q are distinct prime numbers. Find the number of positive integers x ≤pq such that…

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Q: irrational

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Q: Prove that if n is a triangular number, then so are 9n+ 1,25n+ 3, and 49n+ 6. Hint: Recall that in…

A: Triangular numbers are those which are of the form k(k+1)/2 for some natural number k and some…

Q: Let p and q be primes. Prove that pq +1 is a square if and only if p and q are twin primes.

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Q: Find (with proof) all the pairs p, q of positive prime numbers that satisfy p? – 2q? = 1.

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Q: Using the parity theorem and contradiction, prove that for any odd positive integer p,√2p is…

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Q: Is the irrational numbers in (0, 1) countable? Prove your result.

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Q: Prove the statement by contradiction: The square root of 2  divided by 2 is an irrational number.

A: If you have any questions let me know in comment box thankyou for your question.

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.