Take Class 10 Tuition from the Best Tutors
Affordable fees 1-1 or Group class Flexible Timings Verified Tutors Search in
Prove that is irrational.
Asked by Reap Last Modified
Answer 
Let is a rational number. Therefore. we can find two integers a, b (b
0)
such that =
Let a and b have a common factor other than 1. Then we can divide
them by the common factor. and assume that a and b are co-prime.
a = =
Therefore. is divisible by 5 and it can be said that a is divisible by 5. Let a
= 5k. where k is an integer =
=
This mans that
is divisible by 5 and hence, b is divisible
by 5.
This implies that a and b have 5 as a common factor. And this is a
contradiction to the fact that a and b are co-prime.
Hence, cannot be expressed as and it can be said that
is irrational.
Palak Kanti Maitra
I have a degree in Mechanical Engineering I have conducted over 12000 online sessions on Math. durin
Let√5 is a rational number.So √5=a/b, squaring both sides 5=a^2/b^2 and a^2=5b^2,So a^2 is divisible by 5.
Hence a is also divisible by 5. Let a =5c where c is an integer. Then a^2=5b^2=25c^2
b^2=5c^2. So b^2 is divisible by 5. Hence b is also divisible by 5. So and b have a common factor5.But for a rational number a/b ,common factor between a and b cannot be other than 1.So this contradicts √5 is a rational number. So √5 is irrational.
read less
View 3 more Answers
Related Questions
Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com
Ask a QuestionRecommended Articles
Quest Academy - Institute of the month
Quest Academy is a professional Bangalore based NEET and JEE (Main + Advanced) training institute. The academy was incorporated in 2015 to cater to the needs of students, who aim to crack competitive exams by connecting with the best brains around. The institute helps students enhance their skills and capabilities through...
Read full article >
Meet Raghunandan.G.H, a B. Tech Tutor from...
Raghunandan is a passionate teacher with a decade of teaching experience. Being a skilled trainer with extensive knowledge, he provides high-quality BTech, Class 10 and Class 12 tuition classes. His methods of teaching with real-time examples makes difficult topics simple to understand. He explains every concept in-detail...
Read full article >
Meet Sandhya R, a B.Sc tutor from Bangalore
Sandhya is a proactive educationalist. She conducts classes for CBSE, PUC, ICSE, I.B. and IGCSE. Having a 6-year experience in teaching, she connects with her students and provides tutoring as per their understanding. She mentors her students personally and strives them to achieve their goals with ease. Being an enthusiastic...
Read full article >
Meet Swati, a Hindi Tutor from Bangalore
Swati is a renowned Hindi tutor with 7 years of experience in teaching. She conducts classes for various students ranging from class 6- class 12 and also BA students. Having pursued her education at Madras University where she did her Masters in Hindi, Swati knows her way around students. She believes that each student...
Read full article >
Looking for Class 10 Tuition ?
Learn from the Best Tutors on UrbanPro
Are you a Tutor or Training Institute?
Join UrbanPro Today to find students near youThe best tutors for Class 10 Tuition Classes are on UrbanPro
The best Tutors for Class 10 Tuition Classes are on UrbanPro
6
