Find Square Root of Imperfect Numbers in Just 10 Seconds

Duration: 5 min

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Module outline

  1. Quantitative Ability: Percentage, Profit and Loss, Ratio and Proportion (Ratios), Average, Time and Work, Speed Time and Distance, Simple Interest and Compound Interest, Age Problems, Number System, Divisibility Rules, HCF LCM, Algebra, Permutation and Combination, Probability, Data Interpretation, Logarithm, Sequence and Series (Series), Powers and Exponents (Surds and Indices), Speed Mathematics and Basic Mathematics
  2. Logical Reasoning: Seating Arrangements, Puzzle Solving (Puzzles), Data Arrangement, Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Data Sufficiency, Venn Diagram, Inequality, Series (Number and Letter Series) (Numerical Relations and Reasoning), Logical Sequence Of Words, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Analogy, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning)
  3. Verbal Ability: Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Subject Verb Agreement (Verb Noun Agreement), Tenses, Articles, Preposition, Conjunction, Modals, Active Passive Voice (Voice), Direct and Indirect Speech, Vocabulary, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Completion (Fill in the blanks), Sentence Correction (Error Correction), Cloze Test (Cloze Passage), Facts, Inference and Judgements
  4. Programming Fundamentals (Technical): C Fundamentals
  5. Data Structures (Technical): Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  6. Algorithms (Technical): Algorithm Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Time Complexity Analysis, Advanced Algorithms
  7. OOPs (Technical): Object Oriented Programming (OOPS)
  8. DBMS (Technical): Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, ORDBMS, Database Security & Authorization, Query Processing & Optimization, Enhanced Data Models, Data Warehousing & Mining, Big Data Systems, NoSQL
  9. SQL (Technical): SQL
  10. Operating Systems (Technical): Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Linux OS, Security, Distributed Systems, Virtual Machines
  11. Computer Networks (Technical): Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security, Mobile Technology, Cloud Computing and IoT, Cyber and Info Security
  12. Software Engineering (Technical): Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  13. Coding/Automata Round: Coding Questions by Yash Sir, C Programming by Yash Sir, Programming in C++, Java, Python for Placements by Yash Sir, Pseudo Codes
  14. Personality / Behavioral Assessment: Behavioral Assessment (Behavioral Competency Profiling) (Psychometric Test)
  15. Writing Assessment: English Writing Ability
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video, titled 'SPEED MATHS', teaches a rapid method for estimating the square roots of numbers. The instructor, Yash Jain Sir, begins by introducing a table of squares from 1 to 10, which serves as a reference. The core technique involves identifying the two perfect squares between which the target number lies. For example, to find the square root of 66, the instructor notes it is between 64 (8^2) and 81 (9^2). He then uses a formulaic approach: the lower perfect square (64) is subtracted from the target (66), giving a remainder of 2. This remainder is divided by twice the square root of the lower perfect square (2 * 8 = 16), resulting in 2/16 or 0.125. This decimal is added to the integer part (8), yielding an approximation of 8.125. The video demonstrates this method with several examples, including 40, 147, and 175, and concludes by showing the actual calculator values to validate the accuracy of the estimation technique.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card for 'SPEED MATHS' and then transitions to a whiteboard-style presentation. The instructor, Yash Jain Sir, introduces the topic of finding square roots. A table of squares from 1 to 10 is displayed on the left. The instructor begins the first example by stating the number 66. He identifies that 66 lies between 64 (8^2) and 81 (9^2). He circles the number 8 and 64 in the table, establishing the lower perfect square. He then writes the formula '√66 = 8 + 2/16' on the board, where 2 is the difference between 66 and 64, and 16 is twice the square root of 64 (2*8). He explains that this fraction (2/16) simplifies to 0.125, which is added to 8 to get the final approximation of 8.125.

  2. 2:00 – 5:00 02:00-05:00

    The instructor proceeds to demonstrate the method with a second example, the number 40. He identifies that 40 is between 36 (6^2) and 49 (7^2). He circles 6 and 36 in the table. He writes the formula '√40 = 6 + 4/12', where 4 is the difference (40-36) and 12 is twice the square root of 36 (2*6). He simplifies 4/12 to 1/3, which is approximately 0.33, and adds it to 6, giving an approximation of 6.33. He then moves to the third example, 147. He identifies it is between 144 (12^2) and 169 (13^2). He writes '√147 = 12 + 3/24', where 3 is the difference (147-144) and 24 is twice the square root of 144 (2*12). He simplifies 3/24 to 1/8, or 0.125, and adds it to 12, resulting in 12.125. For the final example, 175, he identifies it is between 169 (13^2) and 196 (14^2). He writes '√175 = 13 + 6/26', where 6 is the difference (175-169) and 26 is twice the square root of 169 (2*13). He simplifies 6/26 to 3/13, which is approximately 0.23, and adds it to 13, giving 13.23. Throughout these examples, he uses a calculator to show the actual square root values for comparison.

  3. 5:00 – 5:02 05:00-05:02

    The video concludes with a final screen displaying the text 'THANKS FOR WATCHING' in large white letters against a dark blue, abstract background with faint mathematical equations. This is a standard closing slide for the educational content.

The video presents a structured, step-by-step tutorial on a speed math technique for approximating square roots. The core of the method is a formula derived from linear interpolation: √N ≈ a + (N - a²) / (2a), where 'a' is the integer square root of the nearest perfect square less than N. The lesson progresses from a simple example (66) to more complex ones (40, 147, 175), consistently applying the same logic. The use of a pre-existing table of squares (1-10) is a key pedagogical tool, allowing for quick identification of the base value 'a'. The instructor reinforces the method by comparing the estimated results with the precise values from a calculator, demonstrating the technique's effectiveness for quick mental calculations. The overall flow is logical, moving from concept to application, and is designed to be easily understood and replicated by students.

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