Ncert solutions mathematics class 8 Solutions for Chapter 6 squares and square roots

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:

11^2=121

101^2=10201

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.

(ii) 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

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.

i. 252

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:

(i) 525

(ii) 1750

(iii) 252

(iv) 1825

(v) 6412

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?