No products in the cart.

Prove that sqrt 5 is irrational

CBSE, JEE, NEET, CUET

Question Bank, Mock Tests, Exam Papers

NCERT Solutions, Sample Papers, Notes, Videos

Install Now

Prove that sqrt 5 is irrational

Posted by Kumar Shubham 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Let take √5 as a rational number
If a and b are two co-prime number and b is not equal to 0.
We can write √5 = a/b
Multiply by b both side we get
b√5 = a
To remove root, Squaring on both sides, we get
5b² = a² ……………(1)
Therefore, 5 divides a² and according to a theorem of rational number, for any prime number p which is divided 'a²' then it will divide 'a' also.
That means 5 will divide 'a'. So we can write
a = 5c
and putting the value of a in equation (1) we get
5b² = (5c)²
5b² = 25c²
Divide by 25 we get
b^2/5 = c²
again using the same theorem we get that b will divide by 5
and we have already get that a is divided by 5
but a and b are co-prime number. so it is contradicting.
Hence √5 is an irrational number

1Thank You

ANSWER

Test

Related Questions

(A + B )²

Posted by Abhishek Gupta 1 month, 2 weeks ago

CBSE > Class 10 > Mathematics

1 answers

Prove that root 8 is an irration number

Posted by Sahil Sahil 1 year, 4 months ago

CBSE > Class 10 > Mathematics

2 answers

X-y=5

Posted by Kishan Thakur 1 month ago

CBSE > Class 10 > Mathematics

1 answers

If 1/2 is a root of equation x^2+kx- 5/4 =0 , then what is the value of k

Posted by Parinith Gowda Ms 3 months, 2 weeks ago

CBSE > Class 10 > Mathematics

1 answers

Venu Gopal has twice

Posted by Lakshay Kumar 1 year ago

CBSE > Class 10 > Mathematics

0 answers

This content has been hidden. One or more users have flagged this content as inappropriate. Once content is flagged, it is hidden from users and is reviewed by myCBSEguide team against our Community Guidelines. If content is found in violation, the user posting this content will be banned for 30 days from using Homework help section. Suspended users will receive error while adding question or answer. Question comments have also been disabled. Read community guidelines at https://mycbseguide.com/community-guidelines.html

Few rules to keep homework help section safe, clean and informative.

Don't post personal information, mobile numbers and other details.
Don't use this platform for chatting, social networking and making friends. This platform is meant only for asking subject specific and study related questions.
Be nice and polite and avoid rude and abusive language. Avoid inappropriate language and attention, vulgar terms and anything sexually suggestive. Avoid harassment and bullying.
Ask specific question which are clear and concise.

Remember the goal of this website is to share knowledge and learn from each other. Ask questions and help others by answering questions.

Posted by Hari Anand 6 months, 1 week ago

CBSE > Class 10 > Mathematics

0 answers

Is it possible to design a rectangular mango Grove whose length is twice it's breadth, and the area is 800m²? If so, find it's length and breadth

Posted by Akshata Choukse 1 year, 4 months ago

CBSE > Class 10 > Mathematics

0 answers

Don't post personal information, mobile numbers and other details.
Don't use this platform for chatting, social networking and making friends. This platform is meant only for asking subject specific and study related questions.
Be nice and polite and avoid rude and abusive language. Avoid inappropriate language and attention, vulgar terms and anything sexually suggestive. Avoid harassment and bullying.
Ask specific question which are clear and concise.

Remember the goal of this website is to share knowledge and learn from each other. Ask questions and help others by answering questions.

Posted by Kanika . 1 month ago

CBSE > Class 10 > Mathematics