Class 8 Maths - BIHAR
A Square and A Cube
The chapter 'A Square and A Cube' in Class 8 Mathematics introduces students to the fundamental concepts of squares, square roots, cubes, and cube roots of numbers. Students will learn how to identify perfect squares and cubes, find their values through prime factorization and division methods, and apply these concepts to solve real-life geometrical and arithmetic problems. This chapter is vital for the Bihar Board exams as it forms the strong mathematical foundation needed for higher classes, algebra, and mensuration. Scoring well in this chapter is easy if students memorize basic squares and cubes up to 20 and 10 respectively.
Start Learning FreeKey Concepts
Square of a Number
When a number is multiplied by itself, the product is called the square of that number, written as x squared (x^2).
Square Root
The square root of a number is that value which, when multiplied by itself, gives the original number. It is denoted by the symbol √.
Cube of a Number
When a number is multiplied by itself three times, the product is called the cube of that number, written as x cubed (x^3).
Cube Root
The cube root of a number is the value that, when multiplied by itself three times, gives the original number. It is denoted by the symbol ∛.
Properties of Square Numbers
Square numbers always end in digits 0, 1, 4, 5, 6, or 9 at units place, and a number ending in 2, 3, 7, or 8 is never a perfect square.
Important Formulas
Board Exam Info
In the Bihar Board Class 8 Mathematics examination, this chapter typically carries around 6 to 8 marks. Common question types include finding square roots and cube roots using prime factorization, finding 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 quickly find if a large number is a perfect square?
Check the last digit. If it ends in 2, 3, 7, or 8, it is definitely not a perfect square. Otherwise, use the prime factorization method.
What is the difference between square root and cube root symbols?
The square root symbol is √ while the cube root symbol is ∛ with a small 3 written in the notch of the root sign.
How do I find the smallest number to multiply to make a number a perfect cube?
Find the prime factors of the number and group them in triplets. The factors that do not form a complete triplet are the ones you need to multiply by.
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