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
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
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
Q2) The following numbers are obviously not perfect squares. Give reasons.
(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 an odd number:
(i) 431
(ii) 2826
(iii) 7779
(iv) 82004
The squares of which of the following would be odd numbers?
i. 431
ii. 2826
iii. 7779
iv. 82004
Observe the following pattern and find the missing numbers.
\begin{array}{l} 11^{2}=121 \\ 101^{2}=10201 \\ 1001^{2}=1002001 \\ 100001^{2}=1 \ldots 2\ldots . .1 \\ 10000001^{2}=\ldots \ldots \ldots \ldots . \end{array}
Q4) Observe the following pattern and find the missing digits:
11^2=121
101^2=10201
1001^2=1002001
100001^2=1…..2…..1
1000000^2=1………….
Observe the following pattern and supply the missing numbers.
\begin{array}{l} 11^{2}=121 \\ 101^{2}=10201 \\ 10101^{2}=102030201 \\ 1010101^{2}=\ldots \ldots \ldots \ldots \ldots . . . \end{array}
\ldots \ldots^2=10203040504030201
Q5) Observe the following pattern and supply the missing numbers:
10101^2=102030201
1010101^2=…………………………
……………………^2=10203040504030201
Q6) Using the given pattern, find the missing numbers:
1^2+2^2+2^2=3^2
2^2+3^2+6^2=7^2
3^2+4^2+12^2=13^2
4^2+5^2+_-\ ^2=\ 21^2
5^2+_-\ ^2+30^2=31^2
6^2+_-\ ^2+_-\ ^2=43^2
Using the given pattern, find the missing numbers.
Q7) Without adding, find the sum.
(i) 1 + 3 + 5 + 7 + 9
(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19
(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
Without adding, find the sum.
i. 1 + 3 + 5 + 7 + 9
ii. 1 + 3 + 5 + 7 + 9 + I1 + 13 + 15 + 17 +19
iii. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
Q8) (i) Express 49 as the sum of 7 odd numbers.
(ii) Express 121 as the sum of 11 odd numbers.
(i) Express 49 as the sum of 7 odd numbers.
How many numbers lie between squares of the following numbers?
i. 12 and 13
ii. 25 and 26
iii. 99 and 100
Q9) How many numbers lie between squares of the following numbers:
(i) 12 and 13
(ii) 25 and 26
(iii) 99 and 100
Q1) Find the square of the following numbers.
(i) 32
(ii) 35
(iii) 86
(iv) 93
(v) 71
(vi) 46
Find the square of the following numbers.
i. 32
ii. 35
iii. 86
iv. 93
v. 71
vi. 46
Q2) Write a Pythagoras triplet whose one member is:
(i) 6
(ii) 14
(iii) 16
(iv) 18
Write a Pythagorean triplet whose one member is.
i. 6
ii. 14
iii. 16
iv. 18
Q1) What could be the possible ‘ones’ digits of the square root of each of the following numbers:
(i) 9801
(ii) 99856
(iii) 998001
(iv) 657666025
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
Without doing any calculation, find the numbers which are surely not perfect squares.
i. 153
ii. 257
iii. 408
iv. 441
Q2) Without doing any calculation, find the numbers which are surely not perfect squares:
(i) 153
(ii) 257
(iii) 408
(iv) 441
Q3) Find the square roots of 100 and 169 by the method of repeated subtraction.
Find the square roots of 100 and 169 by the method of repeated subtraction.
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
Q4) Find the square roots of the following numbers by the Prime Factorization method:
(i) 729
(ii) 400
(iii) 1764
(iv) 4096
(v) 7744
(vi) 9604
(vii) 5929
(viii) 9216
(ix) 529
(x) 8100
Q5) 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
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
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.
ii. 2925
iii. 396
iv. 2645
v. 2800
vi. 1620
Q6) 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
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.
Q7) The students of class VIII of a school donated ` 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.
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.
Q9) Find the smallest square number that is divisible by each of the numbers 4, 9 and 10.
Find the smallest square number that is divisible by each of the numbers 4, 9 and 10.
Find the smallest square number that is divisible by each of the numbers 8, 15 and 20.
Q10) Find the smallest square number that is divisible by each of the numbers 8, 15 and 20.
Find the square root of each of the following numbers by Division method.
i. 2304
ii. 4489
iii. 3481
iv. 529
v. 3249
vi. 1369
vii. 5776
viii. 7921
ix. 576
x. 1024
xi. 3136
xii. 900
Q1) Find the square roots of each of the following numbers by Division method:
(i) 2304 (ii) 4489
(iii) 3481 (iv) 529
(v) 3249 (vi) 1369
(vii) 5776 (viii) 7921
(ix) 576 (x) 1024
(xi) 3136 (xii) 900
Find the number of digits in the square root of each of the following numbers (without any calculation).
i. 64
ii. 144
iii. 4489
iv. 27225
v. 390625
Q2) Find the number of digits in the square root of each of the following numbers (without any calculation):
(i) 64
(ii) 144
(iii) 4489
(iv) 27225
(v) 390625
Find the square root of the following decimal numbers.
i. 2.56
ii. 7.29
iii. 51.84
iv. 42.25
v. 31.36
Q3) Find the square root of the following decimal numbers:
(i) 2.56
(ii) 7.29
(iii) 51.84
(iv) 42.25
(v) 31.36
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
iii. 3250
iv. 825
v. 4000
Q4) 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
(iii) 3250
(iv) 825
(v) 4000
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) 1750
(iii) 252
(iv) 1825
(v) 6412
Q5) 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:
Q6) Find the length of the side of a square whose area is 441m^2?
Find the length of the side of a square whose area is 441 \mathrm{m}^{2}.
Q7) In a right triangle ABC, \angle B=90\degree.
(i) If AB = 6 cm, BC = 8 cm, find AC.
(ii) If AC = 13 cm, BC = 5 cm, find AB.
In a right triangle ABC, ∠B = 90^{\circ}.
a. If AB = 6 cm, BC = 8 cm, find AC
b. If AC = 13 cm, BC = 5 cm, find AB
A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this.
Q8) A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remains the same. Find the minimum number of plants he needs more for this.
There are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement.
Q9) There are 500 children in a school. For a P.T. drill, they have to stand in such a manner that the number of rows is equal to the number of columns. How many children would be left out in this arrangement?
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