Find Square Root of Imperfect Numbers in Just 10 Seconds

Duration: 5 min

This video lesson is available to enrolled students.

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Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Paper-1 & 2 | Basic Numeracy: अनुपात और समानुपात / Ratio and Proportion, Divisibility Rules, मिश्रण और एलिगेशन / Mixture and Alligation, Permutation and Combination, Logarithm, संख्या पद्धति / Number System, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, Sequence and Series (Series), समय, चाल और दूरी / Time, Speed and Distance, प्रतिशत / Percentage, औसत / Average, घन क्षेत्रमिति / Solid Mensuration, Age Problems, Arithmetic, Statistics, Probability, लाभ, हानि और बट्टा / Profit, Loss and Discount, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, Partnership, Speed Mathematics and Basic Mathematics, Algebra, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, समय और कार्य / Time and Work, Pipe and Cistern, RSSB Specific Videos - Basic Numeracy, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics, संख्या पद्धति और संख्या सिद्धांत / Number Systems and Number Theory, निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति / Coordinate Geometry, Vectors and 3D Geometry, बहुपद, समीकरण और सम्मिश्र संख्याएँ / Polynomials, Equations and Complex Numbers
  3. Paper-1 & 2 | Data Interpretation: आँकड़ा निर्वचन / Data Interpretation
  4. Paper-1 & 2 | General Mental Ability: Mental Ability, RSSB Specific Videos - Mental Ability
  5. Paper-1 & 2 | Logical Reasoning and Analytical Ability: श्रेणी / Series, कूट लेखन एवं कूट वाचन / Coding-Decoding, Data Sufficiency, अशाब्दिक तर्क / Non-Verbal Reasoning, Syllogisms, बैठक व्यवस्था एवं पहेलियाँ / Seating Arrangement and Puzzles, रक्त संबंध / Blood Relations, दिशा एवं दूरी / Direction and Distance, Analytical Reasoning (Counting Figures Reasoning), गणितीय संक्रियाएँ एवं लुप्त संख्या / Mathematical Operations and Missing Numbers, कैलेंडर एवं घड़ी / Calendar and Clock, Clock, घन, पासा एवं आकृतियों की गिनती / Cubes, Dice and Figure Counting, वेन आरेख, न्याय वाक्य एवं असमानता / Venn Diagrams, Syllogism and Inequalities, सादृश्यता एवं वर्गीकरण / Analogy and Classification, क्रम एवं रैंकिंग / Order and Ranking, कथन आधारित तार्किक विवेचन / Statement-Based Reasoning, Data Arrangement, वर्णमाला एवं संख्या परीक्षण / Alphabet and Number Test, Crypt Arithmetic
  6. Paper-1 & 2 | Decision Making and Problem Solving: आँकड़ों की पर्याप्तता एवं निर्णय क्षमता / Data Sufficiency and Decision Making
  7. Paper-1 | General Science: वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research, Biology, Chemistry, RSSB Specific Videos
  8. Paper-1 | General Awareness: राज्य विशेष सामान्य ज्ञान / State-Specific General Knowledge, समसामयिकी / Current Affairs
  9. Paper-2 | Fundamentals of Computer: Basics of COA, Number System, Floating Point Rep, Number Representation
  10. Paper - 2 | Digital Logic Systems: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits
  11. Paper-2 | Operating Systems: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Linux OS, Distributed Systems
  12. Paper-2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, File Organization & Indexing, Transaction Management, Concurrency Control
  13. Paper-2 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  14. Paper-2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  15. Paper 2 | Oops, C++, Java: Language Design, OOPS with C++, Java, .Net Programming, Java Fundamentals
  16. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  17. Paper 2 | Emerging Trends and AI: Emerging Tech Trends, कंप्यूटर के मूल सिद्धांत / Computer Fundamentals, व्यापार, विपणन एवं उपभोक्ता संरक्षण / Trade, Marketing and Consumer Protection, कंप्यूटर नेटवर्क / Computer Networks
  18. Paper-2 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Advanced Algorithms
  19. Paper 2 | Data Communication and Network Security: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, 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, Ethical Hacking
  20. Paper-2 I Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  21. Paper-2 | Computer Organization and Architecture: Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations
  22. Paper-2 | Web Development: JavaScript-Basics, HTML Basics, CSS, XML
  23. Pedagogy: वृद्धि और विकास / Growth and Development, Concept of Pedagogy, संज्ञानात्मक प्रक्रियाएँ / Cognitive Processes, विकास के सिद्धांत / Theories of Development, समावेशी शिक्षा / Inclusive Education, Experiential Pedagogy, समाजीकरण और जेंडर / Socialisation and Gender, National Education Policy (NEP) 2020
  24. Live Sessions: RSSB Live Sessions
  25. RSSB Paper 1 - Full Mock Tests:
  26. RSSB Paper 2 - Full Mock Tests:
  27. SCI Previous Year Papers:
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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