Q31 of 40 Page 1

Given that √3 is an irrational number, show that (5+2√3) is an irrational number.

OR


An army contingent of 612 members is too much behind an army band of 48 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?


Let 5 + √3 be a rational number then it can be written in the

form


Where p and q are coprime integers.



(p – 5q) and ‘q’ are integers, therefore RHS is a rational number


⇒ √3 is a rational number which is a contradiction.


∴ our assumption is wrong and 5 + 2√3 is an irrational number.


OR


Suppose, both groups are arranged in 'n' columns, for completely filling each column,
The maximum no of columns in which they can march is the highest common factor of their number of members. i.e. n = HCF(612, 48)


Now,


612 = 48 × 12 + 36


48 = 36 × 1 + 12


36 = 12 × 3 + 0


∴ n = HCF(612, 48) = 12


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To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pot have been placed at a distance 1 m from each other along AD, as shown in Fig. 5. Niharika runs 1/4 th the distance AD on the 2nd line and posts are green flag. Preet runs 1/5th the distance AD on the eight line and posts a red flag.

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