• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar
  • Skip to footer

CBSE Tuts

CBSE Maths notes, CBSE physics notes, CBSE chemistry notes

  • NCERT Solutions
    • NCERT Solutions for Class 12 English Flamingo and Vistas
    • NCERT Solutions for Class 11 English
    • NCERT Solutions for Class 11 Hindi
    • NCERT Solutions for Class 12 Hindi
    • NCERT Books Free Download
  • TS Grewal
    • TS Grewal Class 12 Accountancy Solutions
    • TS Grewal Class 11 Accountancy Solutions
  • CBSE Sample Papers
  • NCERT Exemplar Problems
  • English Grammar
    • Wordfeud Cheat
  • MCQ Questions

Finding Square Root of a Perfect Square by Prime Factorization

Square Root Of A Perfect Square By Prime Factorization :

In order to find the square root of a perfect square by prime factorization, follow the following steps.
Step I– Obtain the given number.
Step II– Resolve the given number into prime factors by successive division.
Step III– Make pairs of prime factors such that both the factors in each pair are equal. Since the number is a perfect square, you will be able to make an exact number of pairs of prime factors.
Step IV– Take one factor from each pair.
Step V– Find the product of factors obtained in step IV.
Step VI– The product obtained in step V is the required square root.

Sum and products of roots calculator.

Illustrative Examples :

Square-Root-of-a-Perfect-Square-by-Prime-Factorization-example-1Example 1 : Find the square root of 576.
Solution : By prime factorization,
we get 576=(2 x 2) x (2 x 2) x (2 x 2) x (3 x 3)                            [ Make pairs of factors]
\( \therefore \)   \( \sqrt { 576 } \) = 2x2x2x3 = 24     [ Pickup one factor from each pair ]

 

 

 

Square-Root-of-a-Perfect-Square-by-Prime-Factorization-example-2 Example 2: Find the square root of \( \sqrt { 7744 } \)
Solution: Step 1. Split the given number into prime factors.
7744 =2x2x2x2x2x2x11x11

  Step 2. Form pairs of like factors.
7744 =(2×2)x(2×2)x(2×2)x(11×11)

 

 

Step 3. From each pair. pick out one prime factor

1st pair              2nd pair           3rd pair            4th pair
                              (2×2)       x            (2×2)          x     (2×2)           x      (11×11)
Pick out                Pick out              Pick out               Pick out
one 2                    one 2                    one 2                     one 2

Step 4. Multiply the factors so picked.

The product is the square root of the given number.
\( \sqrt { 7744} \) =2x2x2x11 = 88.

Primary Sidebar

NCERT Exemplar problems With Solutions CBSE Previous Year Questions with Solutoins CBSE Sample Papers
  • The Summer Of The Beautiful White Horse Answers
  • Job Application Letter class 12 Samples
  • Science Lab Manual Class 9
  • Letter to The Editor Class 12 Samples
  • Unseen Passage For Class 6 Answers
  • NCERT Solutions for Class 12 Hindi Core
  • Invitation and Replies Class 12 Examples
  • Advertisement Writing Class 11 Examples
  • Lab Manual Class 10 Science

Recent Posts

  • Understanding Diversity Question Answer Class 6 Social Science Civics Chapter 1 NCERT Solutions
  • Our Changing Earth Question Answer Class 7 Social Science Geography Chapter 3 NCERT Solutions
  • Inside Our Earth Question Answer Class 7 Social Science Geography Chapter 2 NCERT Solutions
  • Rulers and Buildings Question Answer Class 7 Social Science History Chapter 5 NCERT Solutions
  • On Equality Question Answer Class 7 Social Science Civics Chapter 1 NCERT Solutions
  • Role of the Government in Health Question Answer Class 7 Social Science Civics Chapter 2 NCERT Solutions
  • Vital Villages, Thriving Towns Question Answer Class 6 Social Science History Chapter 9 NCERT Solutions
  • New Empires and Kingdoms Question Answer Class 6 Social Science History Chapter 11 NCERT Solutions
  • The Delhi Sultans Question Answer Class 7 Social Science History Chapter 3 NCERT Solutions
  • The Mughal Empire Question Answer Class 7 Social Science History Chapter 4 NCERT Solutions
  • India: Climate Vegetation and Wildlife Question Answer Class 6 Social Science Geography Chapter 8 NCERT Solutions
  • Traders, Kings and Pilgrims Question Answer Class 6 Social Science History Chapter 10 NCERT Solutions
  • Environment Question Answer Class 7 Social Science Geography Chapter 1 NCERT Solutions
  • Understanding Advertising Question Answer Class 7 Social Science Civics Chapter 7 NCERT Solutions
  • The Making of Regional Cultures Question Answer Class 7 Social Science History Chapter 9 NCERT Solutions

Footer

Maths NCERT Solutions

NCERT Solutions for Class 12 Maths
NCERT Solutions for Class 11 Maths
NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 9 Maths
NCERT Solutions for Class 8 Maths
NCERT Solutions for Class 7 Maths
NCERT Solutions for Class 6 Maths

SCIENCE NCERT SOLUTIONS

NCERT Solutions for Class 12 Physics
NCERT Solutions for Class 12 Chemistry
NCERT Solutions for Class 11 Physics
NCERT Solutions for Class 11 Chemistry
NCERT Solutions for Class 10 Science
NCERT Solutions for Class 9 Science
NCERT Solutions for Class 7 Science
MCQ Questions NCERT Solutions
CBSE Sample Papers
NCERT Exemplar Solutions LCM and GCF Calculator
TS Grewal Accountancy Class 12 Solutions
TS Grewal Accountancy Class 11 Solutions