No products in the cart.

  1. Homework Help
  2. CBSE
  3. Class 10
  4. Mathematics

Prove that √p+√q is irrational ,if …

CBSE, JEE, NEET, CUET

CBSE, JEE, NEET, CUET

Question Bank, Mock Tests, Exam Papers

NCERT Solutions, Sample Papers, Notes, Videos

Install Now
Prove that √p+√q is irrational ,if p and q are prime numbers . Explain it with easy method

    • Posted by Dinesh Singh 5 years, 4 months ago

    CBSE > Class 10 > Mathematics
    • 3 answers

    ? Pranali.A.P ? 5 years, 4 months ago

    Search Results Featured snippet from the web Now x, x², p, q and 2 are all rational, and rational numbers are closed under subtraction and division. So (x² - p - q) / 2 is rational. But since p and q are both primes, then pq is not a perfect square and therefore √(pq) is not rational. But this is a contradiction.

    0Thank You

    Yogita Ingle 5 years, 4 months ago

    lets assume that √p is rational,

    ⇒ √p = a/b ( where 'a' and 'b' are co primes, meaning they don't have any common factors except for 1)

    From squaring both sides,

    p = a²/b²

    ⇒pb² = a²

    ⇒ b² = a²/p

    Since 'p' divides a², it also divides 'a' meaning 'a' has a factor of p

    Let 'a' = pm (where m is a positive integer) ⇒ a² = p²m²

    Now, pb² = a²

    pb² = p²m²

    pb²/p²= m²

    b²/p =m²

    ∴ 'p' divides 'b' ⇒ 'b' also has a factor 'p'

    ∴ 'a' and 'b' are not co primes and our assumption was wrong

    ⇒ √p is irrational

    Similarly √q is irrational

    ∴⇒ √p + √q is irrational

    0Thank You

    Sumesh ☺️☺️☺️ 5 years, 4 months ago

    Let us suppose that √p + √q is rational.  Let √p + √q = a, where a is rational.  = √q = a – √p  Squaring on both sides, we get  q = a2 + p - 2a√p => √p = (a2 + p - q)/2a, which is a contradiction as the right hand side is rational number, while√p is irrational.  Hence, √p + √q is irrational.

    2Thank You

    ANSWER
    https://examin8.com Test

    Related Questions

    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 2 months, 2 weeks ago

    CBSE > Class 10 > Mathematics
    • 1 answers
    sin60° cos 30°+ cos60° sin 30°

    • Posted by Vanshika Bhatnagar 1 year, 3 months ago

    CBSE > Class 10 > Mathematics
    • 2 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 5 months, 1 week ago

    CBSE > Class 10 > Mathematics
    • 0 answers
    X-y=5

    • Posted by Kishan Thakur 6 days, 12 hours 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, 3 months ago

    CBSE > Class 10 > Mathematics
    • 0 answers
    (A + B )²

    • Posted by Abhishek Gupta 3 weeks, 3 days ago

    CBSE > Class 10 > Mathematics
    • 1 answers
    Find the nature of quadratic equation x^2 +x -5 =0

    • Posted by Parinith Gowda Ms 2 months, 2 weeks 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 Kanika . 6 days, 12 hours ago

    CBSE > Class 10 > Mathematics
    • 1 answers
    Prove that root 8 is an irration number

    • Posted by Sahil Sahil 1 year, 3 months ago

    CBSE > Class 10 > Mathematics
    • 2 answers

    myCBSEguide App

    myCBSEguide

    Trusted by 1 Crore+ Students

    Install Now

    Test Generator

    Test Generator

    Create papers online. It's FREE.

    Try Now

    CUET Mock Tests

    CUET Mock Tests

    75,000+ questions to practice only on myCBSEguide app

    Install Now
    Google Play

    Download myCBSEguide App

    All Courses

    Other Websites

    CBSE Courses

    Resources

    Corporate

    NCERT Solutions

    CBSE Sample Papers

    All Content and Intellectual Property is under Copyright Protection | myCBSEguide.com ©2007-2025