(a) Use proof by contradiction to show that Proof by contradiction: Suppose √2 1012 +3 is rational Therefore, (b) Enter By definition of rational ✓, there are integers a and b with b# 0 such that √2 1012 +3= b Solve this equation for √2 to obtain √2 = ( √2 1012 2 va 1012 + 3 is irrational. + 3 is irrational. Now the numerator of this fraction in an integer because products and differences of integers are integers, and the denominator is a nonzero integer. Hence, √2 is a quotient of two integers with a nonzero denominator, and so √2 is rational This answer has not been graded vet. a b 1012 √2 + 3 into a handheld calculator with a square root symbol. The result is 1012 ✓by definition of rational ✓. But this result contradicts the fact that √2 is rational ✓, which implies that the supposition is false. which is a rational ✓number. Enter an exact number. (c) Can you use a handheld calculator to determine whether a given quantity is rational? Refer to parts (a) and (b) to write your answer and enter it as a free response. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen