ASSIGNMENT 1 ( SQUARES AND SQUARE ROOTS)
1. What will be the unit digit of the squares of the following numbers?
(i) 81
(ii) 272
(iii) 799
(iv) 3853
(v) 1234
2. The following numbers are obviously not perfect squares. Give reason.
(i) 1057 (ii) 23453 (iii) 7928 (iv) 222222
3. The squares of which of the following would be odd numbers?
(i) 431 (ii) 2826 (iii) 7779 (iv) 82004
4. How many numbers lie between squares of the following numbers?
(i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100
5. Write a Pythagorean triplet whose one member is. (ii) 14 (iii) 16 (iv) 18
6. What could be the possible ‘one’s’ digits of the square root of each of the following numbers?
(i) 9801 (ii) 657666025 (iii) 998001 (iv) 99856
7. 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) 2028 (ii) 180 (iii) 1008 (iv) 1458
8 . 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) 1620 (ii) 2925 (iii) 396 (iv) 2645
SOLVE THE FOLLOWING:
1. 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.
2. 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.
3. Find the square root of the following decimal numbers.(i) 7.29 (ii) 42.25
4. Find the least number which must be subtracted from each of the following numbers so as to
get a perfect square. Also find the square root of the perfect square so obtained.
(i) 402 (ii)
1989
5. Find the least number which must be added to each of the following numbers so as to get a
perfect square. Also find the square root of the perfect square so obtained. (i) 525 (ii) 17
7. Find the smallest number by which 2925 must be divided to get a perfect square. Also, find
the square root of the perfect square so obtained.
8. Find the square root of 63409369
9. The area of a square playground is 291.0436 square meters. Find the length of each side of the
playground.
10. Find the least number that must be added to 506900 to make it a perfect square. Find its
perfect square and its square root.
11. Find the least number of 4 digits that is a perfect square.
12. Find the square root of (a) 14. 10.0469 (b) 15. 0.00038809
13. A decimal fraction is multiplied by itself to give the product 0.007569. Find the decimal
fraction.
ASSIGNMENT 2 (CUBES AND CUBE ROOTS)
1. Find the one’s digit of the cube of 3031
2. Is 32 a perfect cube?
3. Find the cube root of -27000.
4. Find the cube root of 17576 through estimation.
5. Is 5488 a perfect cube? If not, find the smallest natural number by which 5488 must be
multiplied so that the product is a perfect cube.
6. Is 5324 a perfect cube? If not, then by which smallest natural number should 5324 be divided
so that the quotient is a perfect cube?
ASSIGNMENT 3 ( ALGEBRAIC IDENTITIES)
Q1 FIND THE FOLLOWING USING SUITABLE IDENTITIES.
a)
b)
c)
d)
e)
(8x + 3y)2
(0.2x + 1.5y)2
(9.8)2
(85)2-(75)2
103 x 97
Q2 If (4x + 3y) =10 and xy = 4, find the value of (16x2+9y2).
Q3 Factorize x2 + xy – 2xz – 2yz.
Q4 Simplify (6a+5b+4c)2 – (6a- 5b- 4c)2