Class 8 Mathematics Chapter 5 Squares and Square Roots

Report a question

You cannot submit an empty report. Please add some details.

You need to log in to pass this quiz.

I. Chapter Summary:

This chapter helps students understand the concept of squares and square roots of numbers, both perfect and non-perfect squares. It explains methods to find square roots through prime factorization, division method, and estimation techniques. Students also learn about the properties of square numbers, patterns in unit digits, and how to apply these in solving numerical and word problems.

II. Key Concepts Covered:

ConceptExplanation
Perfect SquareA number that is the square of a whole number (e.g., 25 = 5²)
Properties of Square NumbersEnd with 0, 1, 4, 5, 6, 9; never end with 2, 3, 7, or 8
Number of Digits in a SquareDouble or almost double the digits of the original number
Square RootA number which when multiplied by itself gives the original number
Finding Square RootsBy prime factorization, long division, or estimation
Square Roots of DecimalsHandle digits in pairs (before & after the decimal)
Pythagorean TripletsSets of numbers like (3, 4, 5), (5, 12, 13) that satisfy a² + b² = c²

III. Important Questions:

(A) Multiple Choice Questions (1 Mark):

  1. The square of 23 ends in:
    a) 9 ✔️
    b) 5
    c) 6
    d) 3

  2. Which of the following is not a perfect square?
    a) 49
    b) 64
    c) 81
    d) 50 ✔️

  3. The square root of 121 is:
    a) 10
    b) 11 ✔️
    c) 12
    d) 13

  4. If 5² = 25, then √25 is:
    a) 2
    b) 4
    c) 5 ✔️
    d) 6

(B) Short Answer Questions (2/3 Marks):

  1. Find the square root of 324 using prime factorization.

  2. Write five consecutive odd numbers whose squares differ by a fixed amount.

  3. Find the least number to be subtracted from 200 to make it a perfect square.

  4. Is 225 a perfect square? Give reason.

(C) Long Answer Questions (5 Marks):

  1. Find the square root of 2304 by division method.

  2. Find the least number to be added to 525 to make it a perfect square.

  3. Write first five Pythagorean triplets.

  4. Without calculating squares, explain whether 245 can be a perfect square or not.

(D) HOTS (Higher Order Thinking Skills):

  1. A gardener has 1000 plants. He wants to plant them so that each row has the same number of plants. What is the maximum number of complete rows possible?

  2. Prove that square of any odd number is also odd and vice versa.

IV. Key Formulas/Concepts:

ConceptFormula / Rule
Square of a number (n)n² = n × n
Square root of perfect square√x = a, where a × a = x
Square Root of DecimalPair digits from decimal point → left & right, apply division method
Pythagorean Triplet RuleIf m > n, then (m² − n², 2mn, m² + n²) is a triplet

V. Deleted Portions (CBSE 2025–2026):

No portions have been deleted from this chapter as per the rationalized NCERT textbooks.

VI. Chapter-Wise Marks Bifurcation (Estimated – CBSE 2025–2026):

Unit/ChapterEstimated MarksType of Questions Typically Asked
Squares & Square Roots6–8 MarksSquare root methods, Pythagorean triplets, word problems

VII. Previous Year Questions (PYQs):

MarksQuestionYear
3 MarksFind the square root of 1936 by long division2019
2 MarksIs 7921 a perfect square? Give reason2020
5 MarksFind the least number to be added to 3000 to make square2021

VIII. Real-World Application Examples to Connect with Topics:

  • Architecture and Tiling: Square areas are used in design and floor planning.

  • Agriculture: Farmers plant crops in square plots.

  • Physics/Maths: Pythagoras Theorem uses square roots.

  • Computer Programming: Algorithms use square root operations in search & optimization.

IX. Student Tips & Strategies for Success (Class-Specific):

Time Management:

  • Practice square roots by division method daily.

  • Revise squares of 1 to 30 every morning.

Exam Preparation:

  • Focus on prime factorization and spotting non-perfect squares.

  • Solve at least 10 word problems on square roots before exams.

Stress Management:

  • Visual tools like square grids or area models help in conceptual clarity.

  • Use math games and puzzles to keep practice fun.

X. Career Guidance & Exploration (Class-Specific):

For Class 9–10 Students:
StreamCareer Paths
ScienceEngineering, Architecture, Physics Research
CommerceData Analysis, Business Math, Chartered Accountancy
ArtsEducation, Interior Design, Logical Puzzle Design
Explore:

  • Math Olympiads, KVPY, NTSE, NSEJS, Vedic Math Workshops

XI. Important Notes:

  • Always check whether a number ends in 2, 3, 7, 8 — never perfect squares.

  • Use tables, patterns, and visual aids to remember squares quickly.

  • Master division method thoroughly — it’s tested often.

  • Regularly follow ncert.nic.in and cbseacademic.nic.in for official updates.

Translate »