No products in the cart.

Show that there exists no rational …

CBSE, JEE, NEET, CUET

Question Bank, Mock Tests, Exam Papers

NCERT Solutions, Sample Papers, Notes, Videos

Install Now

Show that there exists no rational number whose square is 5

Posted by Sona Budakoti 4 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 4 years, 8 months ago

Given,

Prove that there is no rational number whose square is

Let's assume that , where and and are co-prime.

Then we have,

So,

⇒

This implies that is even.

Then,

So,

⇒

Thus,

⇒

Then,

∴

which contradicts and being co-prime.

Therefore, is irrational.

1Thank You

ANSWER

Related Questions

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 Kanika . 1 month ago

CBSE > Class 10 > Mathematics

1 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, 1 month ago

CBSE > Class 10 > Mathematics

0 answers

Venu Gopal has twice

Posted by Lakshay Kumar 9 months, 3 weeks ago

CBSE > Class 10 > Mathematics

0 answers

sin60° cos 30°+ cos60° sin 30°

Posted by Vanshika Bhatnagar 1 year, 1 month ago

CBSE > Class 10 > Mathematics

2 answers

(A + B )²

Posted by Abhishek Gupta 1 year, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Prove that root 8 is an irration number

Posted by Sahil Sahil 1 year, 1 month ago

CBSE > Class 10 > Mathematics

2 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 Hari Anand 3 months ago

CBSE > Class 10 > Mathematics