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R d sharma solutions mathematics class 8 Solutions for Chapter 3 squares and square roots

Exercises in Chapter 3 squares and square roots Grade 8
Squares and Square Roots Exercise 3.1
Squares and Square Roots Exercise 3.2
Squares and Square Roots Exercise 3.3
Squares and Square Roots Exercise 3.4
Squares and Square Roots Exercise 3.5
Squares and Square Roots Exercise 3.6
Squares and Square Roots Exercise 3.7
Squares and Square Roots Exercise 3.8
Squares and Square Roots Exercise 3.9
Questions in Squares and Square Roots Exercise 3.1

Which of the following numbers are perfect squares?

(i) 484

(ii) 625

(iii) 576

(iv) 941

(v) 961

(vi) 2500

Show that each of the following numbers is a perfect square. Also findthe number whose square is the given number in each case:

(i) 1156

(ii) 2025

(iii) 14641

(iv) 4761

Find the smallest number by which the given number must be multiplied sothat the product is a perfect square:

(i) 23805

(ii) 12150

(iii) 7688

Find the smallest number by which the given number must be divided so that the resulting number is a perfect square:

(i) 12283

(ii) 1800

(iii) 2904

Which of the following numbers are perfect squares?

11, 12, 16, 32, 36, 50, 64, 79, 81, 111, 121

Using prime factorization method, find which of the following numbers are perfect squares?

189, 225, 2048, 343, 441, 2961, 11025, 3549

By what number should each of the following numbers by multiplied to get a

perfect square in each case? Also find the number whose square is the new number.

(i) 8820

(ii) 3675

(iii) 605

(iv) 2880

(v) 4056

(vi) 3468

(vii) 7776

By What numbers should each of the following be divided to get a perfectsquare in each case? Also, find the number whose square is the new number.

(i) 16562

(ii) 3698

(iii) 5103

(iv) 3174

(v) 1575

Find the greatest number of two digits which is a perfect square.

Find the least number of three digits which is perfectsquare.

Find the smallest number by which 4851 must be multiplied so that theproduct becomes a perfect square.

Find the smallest number by which 28812 must be divided so that thequotient becomes a perfect square.

Find the smallest number by which 1152 must be divided so that itbecomes a perfect square. Also find the number whose square is the resulting number.

Questions in Squares and Square Roots Exercise 3.2

The following numbers are not perfect squares. Give reason.

(i) 1547

(ii) 45743

(iii)8948

(iv) 333333

Show that the following numbers are not, perfectsquares:

(i) 9327

(ii) 4058

(iii)22453

(iv) 743522

The square of which of the following numbers would be an old number?

(i) 731

(ii) 3456

(iii)5559

(iv) 42008

What will be the unit’s digit of the squares of the following numbers?

(i) 52

(ii) 977

(iii) 4583

(iv) 78367

(v) 52698

(vi) 99880

(vii) 12796

(viii) 55555

(ix) 53924

Observe the following pattern

1+3 = 22

1+3+5 = 32

1+3+5+7 = 42

And write the value of 1+3+5+7+9+……… up to n terms.

Observe the following pattern

22 -12 = 2 + 1

32 – 22 = 3 + 2

42 – 32 = 4 + 3

52 – 42 = 5 + 4

And find the value of

(i) 1002 -992

(ii)1112 – 1092

(iii) 992 – 96

Which of the following triplets are Pythagorean?

(i) (8, 15, 17)

(ii) (18, 80, 82)

(iii) (14, 48, 51)

(iv) (10, 24, 26)

(v) (16, 63, 65)

(vi) (12, 35, 38)

Observe the following pattern

(1×2) + (2×3) = (2×3×4)/3

(1×2) + (2×3) + (3×4) = (3×4×5)/3

(1×2) + (2×3) + (3×4) + (4×5) = (4×5×6)/3

And find the value of

(1×2) + (2×3) + (3×4) + (4×5) + (5×6)

Observe the following pattern

1 = 1/2 (1×(1+1))

1+2 = 1/2 (2×(2+1))

1+2+3 = 1/2 (3×(3+1))

1+2+3+4 = 1/2 (4×(4+1))

And find the values of each of the following:

(i) 1+2+3+4+5+…+50

(ii) 31+32+….+50

Observe the following pattern

12 = 1/6 (1×(1+1)×(2×1+1))

12+22 = 1/6 (2×(2+1)×(2×2+1)))

12+22+32 = 1/6 (3×(3+1)×(2×3+1)))

12+22+32+42 = 1/6 (4×(4+1)×(2×4+1)))

And find the values of each of the following:

(i) 12+22+32+42+…+102

(ii) 52+62+72+82+92+102+112+122

Which of the following numbers are squares of even numbers?

121, 225, 256, 324, 1296, 6561, 5476, 4489, 373758

By just examining the units digits, can you tell which of the following cannotbe whole squares?

(i) 1026

(ii) 1028

(iii)1024

(iv) 1022

(v) 1023

(vi) 1027

Which of the numbers for which you cannot decide whether they are squares.

Write five numbers which you cannot decide whether they are square just by looking at the unit’s digit.

Write true (T) or false (F) for the following statements.

(i) The number of digits in a square number is even.

(ii) The square of a prime number is prime.

(iii) The sum of two square numbers is a square number.

(iv) The difference of two square numbers is a square number.

(v) The product of two square numbers is a square number.

(vi) No square number is negative.

(vii) There is no square number between 50 and 60.

(viii) There are fourteen square number up to 200.

Questions in Squares and Square Roots Exercise 3.4

Write the possible unit’s digits of the square root of the following numbers. Which of these numbers are odd square roots?

(i) 9801

(ii) 99856

(iii) 998001

(iv) 657666025

Find the square root of each of the following by prime factorization.

(i) 441 (ii) 196

(iii) 529 (iv) 1764

(v) 1156 (vi) 4096

(vii) 7056 (viii) 8281

(ix) 11664 (x) 47089

(xi) 24336 (xii) 190969

(xiii) 586756 (xiv) 27225

(xv) 3013696

Find the smallest number by which 180 must be multiplied so that it becomes a perfect square. Also, find the square root of the perfect square so obtained.

Find the smallest number by which 147 must be multiplied so that it becomes a perfect square. Also, find the square root of the number so obtained.

Find the smallest number by which 3645 must be divided sothat it becomes a perfect square. Also, find the square root of the resulting number.

Find the smallest number by which 1152 must be divided sothat it becomes a square. Also, find the square root of the number so obtained.

The product of two numbers is 1296. If one number is 16 times the other, find the numbers.

A welfare association collected Rs 202500 as donation from the residents. Ifeach paid as many rupees as there were residents, find the number of residents.

A society collected Rs 92.16. Each member collected as many paise as therewere members. How many members were there and how much did each contribute?

A society collected Rs 2304 as fees from its students. If each student paid as many paise as there were students in the school, how many students were therein the school?

The area of a square field is 5184 m2 . A rectangular field, whose length is twice its breadth has its perimeter equal to the perimeter of the square field. Find the area of the rectangular field.

Find the least square number, exactly divisible by each one of the numbers:

(i) 6,9, 15 and 20

(ii) 8, 12, 15 and 20

Find the square roots of 121 and 169 by the method of repeated subtraction.

Write the prime factorization of the following numbers and hence find their square roots.

(i) 7744

(ii) 9604

(iii) 5929

(iv) 7056

The students of class VIII of a school donated Rs 2401 for PM’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.

A PT teacher wants to arrange maximum possible number of 6000 students in a field such that the number of rows is equal to the number of columns. Find the number of rows if 71 were left out after arrangement.

Questions in Squares and Square Roots Exercise 3.5

Find the square root of each of the following by long division method:

(i) 12544 (ii) 97344

(iii) 286225 (iv) 390625

(v) 363609 (vi) 974169

(vii) 120409 (viii) 1471369

(ix) 291600 (x) 9653449

(xi) 1745041 (xii) 4008004

(xiii) 20657025 (xiv) 152547201

(xv) 20421361 (xvi)62504836

(xvii) 82264900 (xviii) 3226694416

(xix) 6407522209 (xx) 3915380329

Find the least number which must be subtracted from the following numbersto make them a perfect square:

(i) 2361

(ii) 194491

(iii) 26535

(iv) 161605

(v) 4401624

Find the least number which must be added to the following numbers tomake them a perfect square:

(i) 5607

(ii)4931

(iii) 4515600

(iv) 37460

(v) 506900

Find the greatest number of 5 digits which is a perfectsquare.

Find the least number of 4 digits which is a perfectsquare.

Find the least number of six digits which is a perfectsquare.

Find the greatest number of 4 digits which is a perfectsquare.

A General arranges his soldiers in rows to form a perfect square. He finds that in doing so, 60 soldiers are left out. If the total number of soldiers be 8160, find the number of soldiers in each row

The area of a square field is 60025m2 . A man cycles along its boundary at 18 Km/hr. In how much time will he return at the starting point?

The cost of levelling and turning a square lawn at Rs 2.50 per m2 is Rs13322.50 Find the cost of fencing it at Rs 5 per metre.

Find the greatest number of three digits which is a perfect square.

Find the smallest number which must be added to 2300 so that it becomes a perfect square.

Questions in Squares and Square Roots Exercise 3.9

Using square root table, find the square roots of the following:

7

Using square root table, find the square roots of the following:

15

Using square root table, find the square roots of the following:

74

Using square root table, find the square roots of the following:

82

Using square root table, find the square roots of the following:

198

Using square root table, find the square roots of the following:

540

Using square root table, find the square roots of the following:

8700

Using square root table, find the square roots of the following:

3509

Using square root table, find the square roots of the following:

6929

Using square root table, find the square roots of the following:

25725

Using square root table, find the square roots of the following:

1312

Using square root table, find the square roots of the following:

4192

Using square root table, find the square roots of the following:

4955

Using square root table, find the square roots of the following:

99/144

Using square root table, find the square roots of the following:

57/169

Using square root table, find the square roots of the following:

101/169

Using square root table, find the square roots of the following:

13.21

Using square root table, find the square roots of the following:

21.97

Using square root table, find the square roots of the following:

110

Using square root table, find the square roots of the following:

1110

Using square root table, find the square roots of the following:

11.11

The area of a square field is 325m2 . Find the approximate length of one side of the field.

Find the length of a side of a square, whose area is equal to the area of a rectangle with sides 240 m and 70 m

Chapters in this book
Rational Numbers
Powers
Squares and Square Roots
Cube and Cube Roots
Playing with Numbers
Algebraic Expressions and Identities
Factorization
Division of Algebraic Expressions
Linear Equation in One Variable
Direct and Inverse Variations
Time and Work
Percentage
Profit Loss Discount and Value Added Tax
Compound Interest
Understanding Shapes Polygons
Understanding Shapes Quadrilaterals
Understanding Shapes Special Types Quadrilaterals
Practical Goemetry
Visualising Shapes
Area of Trapezium and Polygon
Volume Surface Area Cuboid Cube
Surface Area and Volume of Right Circular Cylinder
Classification And Tabulation Of Data
Classification And Tabulation Of Data Graphical Representation Of Data As Histograms
Pictorial Representation Of Data As Pie Charts Or Circle Graphs
Data Handling Probability
Introduction To Graphs
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