SQUARE AND SQUARE
ROOT (Part -1)
Q1 What will be the unit digit of the squares of the following numbers?
(i) 81 (ii) 272 (iii)
799 (iv) 3853 (v) 1234 (vi) 26387 (vii) 52698 (viii) 99880 (ix) 12796
(x) 55555
Q2 The following numbers are obviously not perfect squares. Give reason.
(i) 1057 (ii) 23453
(iii) 7928 (iv) 222222 (v) 64000 (vi) 89722 (vii) 222000 (viii) 505050
Q3 The squares of which of the following would be odd numbers?
(i) 431 (ii) 2826 (iii)
7779 (iv) 82004
Q4 Write a Pythagorean triplet whose smallest member is 8.
Q5 Find a Pythagorean triplet in which one member is 12.
Q6 Write a Pythagorean triplet whose one member is. (i) 6 (ii) 14 (iii) 16 (iv) 18
Q7 Area of a square is 144 cm2. What could be the side of the square?
Q8 What is the length of a diagonal of a square of side 8 cm
Q9 In a right triangle the length of the hypotenuse and a side are
respectively 5 cm and 3 cm
Is 90 a perfect square?
Q10 Is 2352 a perfect
square? If not, find the smallest multiple of 2352 which is a perfect square.
Find the square root of the new number.
Q11 Find the smallest number
by which 9408 must be divided so that the quotient is a perfect square. Find
the square root of the quotient.
Q12 Find the smallest square number which is
divisible by each of the numbers 6, 9 and 15.
Q13 What could be the possible ‘one’s’ digits of
the square root of each of the following
numbers? (i) 9801 (ii)
99856 (iii) 998001 (iv) 657666025
Q14 Without doing any calculation, find the
numbers which are surely not perfect squares.
(i) 153 (ii) 257 (iii)
408 (iv) 441
Q15 Find the square roots of 100 and 169 by the
method of repeated subtraction.
Q16 . Find the square roots of the following
numbers by the Prime Factorisation Method.
(i) 729 (ii) 400 (iii)
1764 (iv) 4096 (v) 7744 (vi) 9604 (vii) 5929
(viii) 9216 (ix) 529 (x) 8100
Q17 For each of the following numbers, find the
smallest whole number by which it should
be multiplied so as to get a perfect square number. Also find the square
root of the square number so obtained. (i) 252 (ii) 180 (iii) 1008 (iv) 2028 (v)
1458 (vi) 768
Q18 For each of the following numbers, find the
smallest whole number by which it should
be divided so as to get a perfect square. Also find the square root of the
square number so obtained. (i) 252
(ii) 2925 (iii) 396 (iv) 2645(v) 2800 (vi) 1620
Q19 The students of Class VIII of a school
donated Rs 2401 in all, for Prime Minister’s
National Relief Fund.
Each student donated as many rupees as the number of students
in the class. Find the
number of students in the class.
Q20 2025 plants are to be
planted in a garden in such a way that each row contains as many plants as the
number of rows. Find the number of rows and the number of plants in each row.
Q21 Find the smallest square number that is
divisible by each of the numbers 4, 9 and 10.
Q22 Find the smallest square number that is
divisible by each of the numbers 8, 15 and 20.
BY
SANJEEV TANEJA
DRP MATH
LUDHIANA
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