Question

(a) Find ten rational number between -25 and 12.   (b) Insert 5 rational numbers and 2 irrational numbers between  √2​ and √3​​​​. [4 MARKS]

Solution

Each part: 2 Marks (a) The LCM of denominator -5 and 2 = -10. Converting these rational numbers to equivalent rational numbers having common denominator. −2×25×2=−410=−4×210×2=−820 1×52×5=510=5×210×2=1020 Clearly -7, -6, -5.............8, 9 are integers between numerators -8 and 10 of these equivalent rational number. Thus we can take any 10 rational numbers and the numbers are −720, −620, −520,−320,−120, 0,120, 320, 420, 520. (b) √2​ = 1.414 (approx) √3​​​​ = 1.732 (approx) 5 rational numbers between  √2​ and √3​​​​ are 1.42, 1.43, 1.44, 1.45, 1.50. (there are many more) 2 irrational numbers between  √2​ and √3​​​​ are  √2.1 and √2.9 (there are many more) Mathematics

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