Surds and Indices Part 4

Duration: 3 min

This video lesson is available to enrolled students.

Return to /learn/ZERO-TO-HERO/aptitude/powers-and-exponents-surds-and-indices/comparing-simplifying-complex-powers/asset-surds-and-indices-part-4 after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control
  2. Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  3. Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  4. Computer Architecture: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design
  5. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Virtual Memory, Disc Scheduling, File Management, Memory Management, Threads & Process Creation
  6. Computer Networks: Introduction to CN, 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, Network Security, Hardware Basics
  7. Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  8. Algorithms: Algorithm Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Time Complexity Analysis
  9. Theory Of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory
  10. Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  11. C language: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums
  12. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  13. Emerging Trends & AI: Emerging Tech Trends, Artificial Intelligence
  14. Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing
  15. Aptitude: Percentage, Ratio and Proportion (Ratios), Logarithm, HCF LCM, Divisibility Rules, Average, Sequence and Series (Series), Number System, Powers and Exponents (Surds and Indices), Algebra, Permutation and Combination, Probability, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Speed Time and Distance, Mixture and Alligation, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Statistics, Data Interpretation, Arithmetic, Speed Mathematics and Basic Mathematics, TCS NQT Advanced Quantitative Ability, Gamified / Game Based Aptitude, Linear Algebra, Trigonometry
  16. Reasoning: Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Crypt Arithmetic, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence, TCS NQT Advanced Reasoning Ability
  17. English (Verbal Ability): Vocabulary, Noun, Pronoun, Adjectives, Preposition, Articles, Direct and Indirect Speech, Tenses, Conjunction, Subject Verb Agreement (Verb Noun Agreement), Modals, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Sentence Construction, Active Passive Voice (Voice), Determiner, Facts, Inference and Judgements, Adverb, Interjection, Verb, English Writing Ability
  18. Engineering Mathematics: Calculus, Vectors
  19. GATE Live Class Recordings 2026: GATE 2026 Live Class
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video, presented by Yash Jain Sir from Knowledge Gate Educator, is a tutorial on solving problems involving infinite nested radicals, specifically focusing on surds and indices. The video begins with a worked example demonstrating the simplification of the square root of 2601 by factoring it into prime factors (3x3x17x17), which is then simplified to 3x17, resulting in 51. The main lesson then transitions to a more complex problem: finding the value of the infinite nested radical y = √(3√(9√(3√(9...)))) where the pattern '3, 9' repeats infinitely. The instructor explains that this expression can be rewritten as y = √(3√(3²√(3√(3²...)))). By recognizing the repeating pattern, he sets up the equation y = √(3√(3²y)), which is then squared to eliminate the outermost radical, leading to y² = 3√(3²y). This is further simplified to y² = 3√(9y), and squaring both sides again yields y⁴ = 9 * 9y, or y⁴ = 81y. Dividing both sides by y (assuming y ≠ 0) gives y³ = 81. Since 81 is 3⁴, the equation becomes y³ = 3⁴. The instructor then solves for y by taking the cube root of both sides, resulting in y = 3^(4/3). The video concludes with a similar example using the number 2, where y = √(2√(4√(2√(4...)))) is solved to find y = 2^(4/3). The final frame is a 'Thanks for Watching' screen.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a whiteboard displaying a math problem: √2601 = √(3x3x17x17), which is simplified to 3x17, resulting in 51. The topic is introduced as 'SURDS & INDICES'. The instructor, Yash Jain Sir, then presents a new problem: y = √(3√(9√(3√(9...)))) with the pattern '3, 9' repeating infinitely. He explains that this can be rewritten as y = √(3√(3²√(3√(3²...)))). He sets up the equation y = √(3√(3²y)) and begins to solve it by squaring both sides, leading to y² = 3√(3²y). He then simplifies this to y² = 3√(9y) and squares both sides again to get y⁴ = 9 * 9y, or y⁴ = 81y. He divides by y to get y³ = 81, and since 81 is 3⁴, he writes y³ = 3⁴. He then circles the number 3 and writes '3' below it, indicating the next step is to solve for y.

  2. 2:00 – 2:42 02:00-02:42

    The instructor continues solving the equation y³ = 3⁴. He explains that to find y, one must take the cube root of both sides, so y = (3⁴)^(1/3) = 3^(4/3). He then presents a similar problem with the number 2: y = √(2√(4√(2√(4...)))) and applies the same method. He rewrites it as y = √(2√(2²√(2√(2²...)))) and sets up the equation y = √(2√(2²y)). He squares both sides to get y² = 2√(2²y), simplifies to y² = 2√(4y), and squares again to get y⁴ = 4 * 4y, or y⁴ = 16y. Dividing by y gives y³ = 16. Since 16 is 2⁴, he writes y³ = 2⁴. He then circles the number 2 and writes '2' below it, indicating the solution is y = 2^(4/3). The video ends with a 'Thanks for Watching' screen.

The video provides a clear, step-by-step demonstration of solving infinite nested radical expressions by leveraging the properties of exponents and indices. The core method involves recognizing the repeating pattern within the radical, which allows the entire expression to be represented as an equation in terms of the variable itself. This self-referential equation is then algebraically manipulated by squaring both sides to eliminate radicals, leading to a polynomial equation that can be solved for the variable. The lesson effectively connects the concepts of surds and indices, showing how to convert radicals into fractional exponents to simplify complex expressions. The progression from a simple numerical example to a more abstract algebraic one reinforces the general applicability of the technique.

Loading lesson…