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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

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 digits

Observe the following pattern and supply the missing numbers

Using the given pattern, find the missing numbers

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

Express 49 as the sum of 7 odd numbers.

Express 121 as the sum of 11 odd numbers

How many numbers lie between squares of the following numbers?

(i) 12 and 13

(ii) 25 and 26

(iii) 99 and 100

Find the square of the following numbers

(i) 32 (ii) 35

(iii) 86 (iv) 93

(v) 71 (vi) 46

Write a Pythagorean triplet whose one member is

(i) 6 (ii) 14

(iii) 16 (iv) 18

What could be the possible ‘one’s’ digits of the square root of each of the followingnumbers?

(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

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 Factorization Method

(i) 729 (ii) 400

(iii) 1764 (iv) 4096

(v) 7744 (vi) 9604

(vii) 5929 (viii) 9216

(ix) 529 (x) 8100

For each of the following numbers, find the smallest whole number by which it shouldbe multiplied so as to get a perfect square number. Also find the square root of thesquare 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 shouldbe divided so as to get a perfect square. Also find the square root of the squarenumber 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

2025 plants are to be planted in a garden in such a way that each row contains asmany plants as the number of rows. Find the number of rows and the number of plants in each row

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

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

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

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 asto 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

Find the length of the side of a square whose area is 441 m^{2}

In a right triangle ABC, ∠B = 90°

(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 numberof rows and the number of columns remain 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 amanner that the number of rows is equal to number of columns. How many childrenwould be left out in this arrangement?