M l aggarwal understanding icse 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

Questions in Squares and Square Roots Exercise 3.1

Which of the following natural numbers are perfect squares? Give reasons in support of your answer.

(i) 729

(ii) 5488

(iii) 1024

(iv) 243

Show that each of the following numbers is a perfect square. Also, find the number whose square is the

given number.

(i) 1296

(ii) 1764

(iii) 3025

(iv) 3969

Find the smallest natural number by which 1008 should be multiplied to make it a perfect square.

Solution:

Find the smallest natural number by which 5808 should be divided to make it a perfect square. Also, find

the number whose square is the resulting number.

Questions in Squares and Square Roots Exercise 3.2

Write five numbers which you can decide by looking at their one’s digit that they are not square

numbers.

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

(i) 951

(ii) 502

(iii) 329

(iv) 643

(v) 5124

(vi) 7625

(vii) 68327

(viii) 95628

(ix) 99880

(x) 12796

The following numbers are obviously not perfect. Give reason.

(i) 567

(ii) 2453

(iii) 5298

(iv) 46292

(v) 74000

The square of which of the following numbers would be an odd number or an even number? Why?

(i) 573

(ii) 4096

(iii) 8267

(iv) 37916

How many natural numbers lie between the square of the following numbers?

(i) 12 and 13

(ii) 90 and 91

Without adding, find the sum.

(i) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15

(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29

(i) Express 64 as the sum of 8 odd numbers.

(ii) 121 as the sum of 11 odd numbers.

Express the following as the sum of two consecutive integers.

$(i) 19^{2} (ii) 33^{2} (iii) 47^{2}$

Find the squares of the following numbers without actual multiplication:

(i) 31

(ii) 42

(iii) 86

(iv) 94

Find the squares of the following numbers containing 5 in unit’s place:

(i) 45

(ii) 305

(iii) 525

Write a Pythagorean triplet whose one number is

(i) 8

(ii) 15

(iii) 63

(iv) 80

Observe the following pattern and find the missing digits:

$\begin{array}{l} 21^{2}=441 \\ 201^{2}=40401 \\ 2001^{2}=4004001 \\ 20001^{2}=4-4-1 \\ 200001^{2}= \end{array}$

Observe the following pattern and find the missing digits

$9^{2}=81$

$\begin{array}{l} 99^{2}=9801 \\ 999^{2}=998001 \\ 9999^{2}=99980001 \\ 99999^{2}=9-8-01 \\ 999999^{2}=9--0-1 \end{array}$

Observe the following pattern and find the missing digits

$\begin{array}{l} 7^{2}=49 \\ 67^{2}=4489 \\ 667^{2}=444889 \\ 6667^{2}=44448889 \\ 66667^{2}=4-8-9 \\ 666667^{2}=4 \ldots-8-8 \end{array}$

Questions in Squares and Square Roots Exercise 3.3

By repeated subtraction of odd numbers starting from 1, find whether the following numbers are perfect

squares or not? If the number is a perfect square then find its square root:

Find the square roots of the following numbers by prime factorization method:

(i) 784

(ii) 441

(iii) 1849

(iv) 4356

(v) 6241

(vi) 8836

(vii) 8281

(viii) 9025

Find the square roots of the following numbers by prime factorization method:

(i) 9 67/121

(ii) 17 13/36

(iii) 1.96

(iv) 0.0064

For each of the following numbers, find the smallest natural number by which it should be multiplied so

as to get a perfect square. Also, find the square root of the square number so obtained:

(i) 588

(ii) 720

(iii) 2178

(iv) 3042

(v) 6300

For each of the following numbers, find the smallest natural number by which it should be multiplied so

as to get a perfect square. Also, find the square root of the square number so obtained:

(i) 588

(ii) 720

(iii) 2178

(iv) 3042

(v) 6300

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Chapters in this book

Rational Numbers

Exponents and Powers

Squares and Square Roots

Cubes and Cube Roots

Playing with Numbers

Operation on sets Venn Diagrams

Percentage

Simple and Compound Interest

Direct and Inverse Variation

Algebraic Expressions and Identities

Factorisation

Linear Equations and Inequalities In one Variable

Understanding Quadrilaterals

Constructions of Quadrilaterals

Circle

Symmetry Reflection and Rotation

Visualising Solid Shapes

Mensuration

Data Handling