Class 8 Maths - HARYANA
A Square and A Cube
The chapter 'Squares and Square Roots, Cubes and Cube Roots' in Class 8 Mathematics for Haryana (BSEH) students builds a strong foundation in number properties. It introduces you to numbers multiplied by themselves and teaches you how to find square roots using prime factorization and division methods. You will also learn about cubic numbers and their cube roots. This chapter is very important for board exams because it forms the basis for algebra, geometry, and advanced arithmetic, frequently appearing in both objective and subjective questions.
Start Learning FreeKey Concepts
Square Number
A square number is obtained by multiplying a whole number by itself, such as 5 × 5 = 25.
Square Root
The square root is the inverse operation of squaring; for example, the square root of 25 is 5 (written as √25 = 5).
Cube Number
A cube number is formed by multiplying a number three times by itself, such as 3 × 3 × 3 = 27.
Cube Root
The cube root of a number is a value that, when multiplied by itself three times, gives that number, denoted by the symbol ∛.
Prime Factorization Method
A method used to find square roots and cube roots by breaking down a composite number into its prime factors and grouping them in pairs or triplets.
Important Formulas
Board Exam Info
In the Haryana Board (BSEH) Class 8 Mathematics exam, this chapter typically carries around 6 to 8 marks. Common question types include finding square roots by long division method, determining the smallest number by which a given number must be multiplied or divided to make it a perfect square or cube, and word problems based on area and volume.
Frequently Asked Questions
How can I easily find if a big number is a perfect square?
Check the units digit of the number. Perfect squares always end in 0, 1, 4, 5, 6, or 9. If it ends in 2, 3, 7, or 8, it is never a perfect square.
What is the difference between prime factorization and long division methods for square roots?
Prime factorization is easier for smaller numbers where you break factors into pairs. Long division is faster and more efficient for larger numbers and numbers that are not perfect squares.
How do I know whether to multiply or divide in 'find the smallest number' questions?
After doing prime factorization, look at the unpaired factors. If a factor is left alone without a pair (or triplet), you multiply by that factor to complete the group, or divide by that extra factor to remove it.
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