Category: Algebra


  • We use roots to express the inverse operation of exponentiation. For example, if we have x², the square root helps us find the original number x when we know x². In other words, the square root of a number x is the value y that, when multiplied x by itself, gives y. Basic rules of…

  • EXPONENTS

    Exponents (also called powers) are a compact way to write repeated multiplication. If a is a real number and n is a positive integer, then ana^nan means a multiplied by itself n times: an=a⋅a⋅⋯⋅a⏟n factors.a^n = \underbrace{a \cdot a \cdot \dots \cdot a}_{n\ \text{factors}}. Here aa is the base and nn is the exponent (or power).…

  • Squaring tricks

    Squaring Numbers Ending with 5 When you square any number ending with 5, the result always ends with 25. There is a quick and easy method to find the square without actually multiplying the entire number. Method: So all you need to calculate is product of numbers before 5 and their follower. Examples: This method…

  • Dividing by 25

    To divide numbers like 24 by 25 in the regular way, you perform the division directly: 24 ÷ 25 = 0.96 This means 24 divided by 25 equals 0.96. A simpler way to divide 24 by 25 is to multiply both numbers by 4 to get an equivalent division problem with 100 as the divisor:…

  • Solving Large Numbers Without Using a Calculator

    In many Olympic-level math competitions and tests, students are often not allowed to use calculators. This rule encourages participants to develop strong mental math skills and a deeper understanding of numerical properties. When faced with large numbers or complex expressions, students learn to simplify problems by breaking them down into smaller, more manageable parts. For…

  • Mathematical Laws You Must Know

    There are several important mathematical laws you need to understand to calculate accurately. In this session, I will cover most of them, but feel free to ask if you want to learn about any others that might not be included. Mostly common mistake 2 + 6 ÷ 3 = 2 + 2 = 4 because…