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Squares and Square Roots Class 8 Maths in One shot with Formula Cheat Sheet | BYJU'S - Class 8

BYJU'S - Class 6, 7 & 8・2 minutes read

The class focuses on revising math concepts for squares and square roots, encouraging consistent practice and participation in the Akash National Talent Hunt Exam. Various methods for finding squares, including the long division method for square roots, Pythagorean triplets, and the importance of prime factorization, are discussed to enhance mathematical skills.

Insights

  • Consistent practice and confidence are key in mastering math concepts, with emphasis on observing patterns in square numbers to enhance problem-solving skills.
  • Utilizing specific techniques like multiplying the square of the digit 5 by the product of the tens place digit and its successor simplifies calculating squares of numbers ending in five, extending to three-digit numbers and ensuring accuracy through a step-by-step process.

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Recent questions

  • How can I improve my math skills?

    Practice consistently and participate in math exams.

  • What are perfect squares?

    Numbers that result from multiplying a number by itself.

  • How can I identify perfect squares?

    Look for patterns in unit digits and endings.

  • What is the Pythagorean theorem?

    The sum of squares of shorter sides equals hypotenuse square.

  • How can I find square roots using long division?

    Utilize the step-by-step method for accurate results.

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Summary

00:00

Mastering Math: Squares, Roots, and Confidence

  • The class is focused on revising math concepts for an upcoming test on squares and square roots.
  • Students are reminded to have their notebooks, pens, and windows open for solving problems together.
  • The teacher emphasizes the importance of consistent practice in math and encourages students not to give up easily.
  • The class discusses the importance of confidence in learning math and the need to avoid negative thoughts.
  • The teacher introduces the concept of perfect squares and explains how to find the area of a square.
  • Students are encouraged to participate in the Akash National Talent Hunt Exam for grades 7 to 12.
  • The teacher provides tips for scoring full marks in math, emphasizing the importance of practice.
  • The class covers the properties of square numbers, including patterns in unit digits and numbers ending in 1 or 9.
  • Students are asked to identify perfect squares based on the properties discussed in the class.
  • The teacher encourages students to observe patterns in square numbers and apply them to solve problems effectively.

14:42

Square Numbers: Patterns, Methods, and Calculations

  • The square of numbers ending in 1 or 9 always ends in 1 (e.g., 1, 9, 11, 19).
  • Challenging questions are available on the channel, with videos posted for reference.
  • Numbers ending in 2, 7, or 8 result in squares ending in the same digit.
  • Squares of numbers ending in 4 or 6 always end in 6 (e.g., 4, 6, 14, 16).
  • The number of zeros in square numbers doubles from the original number (e.g., 100, 10,000).
  • Square numbers always have an even number of zeros at the end.
  • Methods for finding the square of a number include splitting it into tens and units, using the identity formula, and a mental calculation method.
  • Different methods for finding squares include using the identity formula, multiplying the first term with the entire bracket, and a mental calculation method.
  • A mental calculation method involves squaring the digits individually and adding them up.
  • The square of 47 is 2209, calculated using the identity formula or the mental calculation method.

29:35

Squaring Two-Digit Numbers Ending in Five

  • The method discussed involves finding the square of two-digit numbers ending in five, like 25, 35, and 65.
  • To find the square of a number like 65, multiply the square of the digit 5 (25) by the product of the digit 6 and its successor, 7, resulting in 42.
  • This method simplifies the calculation by breaking down the process into smaller steps.
  • The square of numbers ending in five can be found by multiplying the square of the digit 5 by the product of the tens place digit and its successor.
  • The process involves multiplying the tens place digit by its successor and squaring the digit 5 to obtain the final result.
  • The method is applicable to any two-digit number ending in five, providing a straightforward way to calculate the square.
  • The technique extends to three-digit numbers ending in five, maintaining the same principles for calculation.
  • Moving on to Pythagorean triplets, these are sets of three positive integers that satisfy the Pythagorean theorem, such as 3, 4, and 5.
  • The Pythagorean theorem states that the sum of the squares of the two shorter sides of a right-angled triangle equals the square of the hypotenuse.
  • Pythagorean triplets follow a specific pattern, represented as 2m, m^2 - 1, and m^2 + 1, where m is a positive integer.

44:18

"Mastering Multiplication, Perfect Squares, and Roots"

  • Multiplying numbers: 5 times 3 is 15, 3 times 5 is 15, 3 times 2 is 6, 3 times 1 is 3, 3 times 7 is 21, 5 times 5 is 25, 5 times 7 is 35, 7 times 1 is not a perfect square.
  • Perfect square explanation: To create a perfect square, numbers must be in pairs, like 3 times 3, 5 times 5, and 7 times 7.
  • Importance of prime factorization: Prime factorization is crucial and used in various problem-solving scenarios across different subjects.
  • Long division method for finding square roots: Explained using the example of finding the square root of 576 and 529.
  • Step-by-step long division method: Start from the extreme right, make pairs, subtract, double the number, and match the digits for accurate results.
  • Example of finding the square root of 576: Result is 24, achieved by doubling the number and matching the digits.
  • Importance of consistency in numbers: Numbers must be the same in both steps of the long division method for accurate calculations.
  • Formula sheet overview: Includes formulas for square of a two-digit number, product of consecutive even and odd numbers, Pythagorean triplets, and integral square roots of perfect square numbers.
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