No products in the cart.

# prove that √3+ √5 is irrational

## CBSE, JEE, NEET, NDA

Question Bank, Mock Tests, Exam Papers

NCERT Solutions, Sample Papers, Notes, Videos

prove that √3+ √5 is irrational

Himanshu Chauhan 1 month, 1 week ago

Given √3 + √5 To prove: √3 + √5 is an irrational number. Let us assume that√3 + √5 is a rational number. So it can be written in the form a/b √3 + √5 = a/b Here a and b are coprime numbers and b ≠ 0 Solving √3 + √5 = a/b On squaring both sides we get, (√3 + √5)² = (a/b)² √3² + √5² + 2(√5)(√3) = a²/b² 3 + 5 + 2√15 = a²/b² 8 + 2√15 = a²/b² 2√15 = a²/b² – 8 √15 = (a²- 8b²)/2b a, b are integers then (a²-8b²)/2b is a rational number. Then √15 is also a rational number. But this contradicts the fact that √15 is an irrational number. Our assumption is incorrect √3 + √5 is an irrational number. Hence, proved.

Rupesh Rounak 1 month, 1 week ago

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.

Related Questions

## myCBSEguide

Trusted by 1 Crore+ Students

#### Question Paper Creator

• Create papers in minutes
• Print with your name & Logo