CBSE | CBSE Board | Homework Help

Prove that root 2 is an irrational number. Rational numbers are integers that are expressed in the form of p / q where p and q are both co-prime numbers and q is non-zero. Answer: Hence proved that √2 is an irrational number. Let's find if √2 is irrational. Explanation: To prove that √2 is an irrational number, we will use the contradiction method. Let us assume that √2 is a rational number with p and q as co-prime integers and q ≠ 0 ⇒ √2 = p/q On squaring both sides we get, ⇒ 2q2 = p2 ⇒ Here, 2q2 is a multiple of 2 and hence it is even. Thus, p2 is an even number. Therefore, p is also even. So we can assume that p = 2x where x is an integer. By substituting this value of p in 2q2 = p2, we get ⇒ 2q2 = (2x)2 ⇒ 2q2 = 4x2 ⇒ q2 = 2x2 ⇒ q2 is an even number. Therefore, q is also even. Since p and q both are even numbers, they have 2 as a common multiple which means that p and q are not co-prime numbers as their HCF is 2. This leads to the contradiction that root 2 is a rational number in the form of p/q with "p and q both co-prime numbers" and q ≠ 0. Thus, √2 is an irrational number by the contradiction method.

5Thank You

ANSWER

Why do we get hurt when we strike a brick but we don't get hurt on beating against water?

Posted by Account Deleted 2 years, 8 months ago

CBSE > Class 09 > Science

0 answers

ANSWER

Draw a brief character sketch of yajnavalkya wife Maitreyi

Posted by Praveen Nagar 2 years, 8 months ago

CBSE > Class 12 > English Elective NCERT

0 answers

ANSWER

The communication process , can be affected negatively by a number of barriers . which one of the following is not an appropriate barrier? (a) feelings (b) Cultural differences (c) language ascent (d) Calligraphy

Posted by Grick Sudrania 2 years, 8 months ago

CBSE > Class 07 > Computer

1 answers

Sagar Taware 2 years, 7 months ago

Feel

0Thank You

ANSWER

The communication process , can be affected negatively by a number of barriers . which one of the following is / are barriers. (a) cultural differences (b) language ascent (c) Technology (d) Calligraphy

Posted by Grick Sudrania 2 years, 8 months ago

CBSE > Class 07 > Computer

0 answers

ANSWER

Once a week, chintan cleans his room . Change into passive voice

Posted by Deepanjali Sharma 2 years, 8 months ago

CBSE > Class 10 > Information Technology (402)

0 answers

ANSWER

Change the active voice to passive voice and vice versa

Posted by Deepanjali Sharma 2 years, 8 months ago

CBSE > Class 10 > Information Technology (402)

0 answers

ANSWER

Who is rushing to the school?

Posted by Satbir Ranga 2 years, 8 months ago

CBSE > Class 05 > English

1 answers

Tanuj Nial 2 years, 8 months ago

Student is rushing to the school

0Thank You

ANSWER

Wars Bring Nothing but Destruction

Posted by Siddu Khatik 2 years, 8 months ago

CBSE > Class 08 > English

0 answers

ANSWER

Kiranon ki Bheed Mein Kaun Kho Gaya

Posted by Akrisht Rajput 2 years, 8 months ago

CBSE > Class 06 > हिंदी (OLD)

0 answers

ANSWER

√12×√15=

Posted by F.786.Firoz 9427392408S 2 years, 8 months ago

CBSE > Class 09 > Mathematics

1 answers

Ashutosh Biswal 2 years, 8 months ago

6√5

0Thank You

ANSWER

What should be added to twice rational number -7/3 to get 3/7

Posted by Manoj Kumar Vishwakarma 2 years, 8 months ago

CBSE > Class 08 > गणित

1 answers

Soheb Ansari 2 years, 8 months ago

Chapter 3 ke questions answer

4Thank You

ANSWER

NV oc ur, hv

Posted by Md Sufail Islam 2 years, 8 months ago

CBSE > Class 09 > Mathematics

0 answers

ANSWER

E_mail

Posted by Tanya Singh Rajpoot 2 years, 8 months ago

CBSE > Class 10 > हिंदी ए

1 answers

Shahjahan Alam 2 years, 8 months ago

Kaha Se ho

1Thank You

ANSWER

Indian grey hornbills found in cities hornbills are found and forested areas. They are omnivorous. (a) They are medium-sized birds are uniformly (b) grey in colour with lighter grey or (C) dull white belly underparts. Like all (d) other hornbills (Malabar grey hornbill (e) is exception), Indian grey hornbills (f) have small back casque or horn on beak extending over the brow. (h)

Posted by Mridul Bhardwaj 2 years, 8 months ago

CBSE > Class 09 > English Lang & Lit. (184)

0 answers

ANSWER

Log8 4

Posted by Rohan Kumar Saw 2 years, 8 months ago

CBSE > Class 11 > Applied Maths

1 answers

Shreysi Prabhat 2 years, 2 months ago

2/3

0Thank You

ANSWER

Can Anyone please tell me that hiw important is " Inverse Trigonometric functions" ( Chapter : 2 ) for class 12th boards ?

Posted by A B 2 years, 8 months ago

CBSE > Class 12 > Mathematics

2 answers

Mannat Thukral 2 years, 8 months ago

What I would suggest is a Brushup and revision of class 11 trigonometry formulas before starting this chapter would be a great benefit as it will help to easily solve the questions and grasp the concepts

0Thank You

Mannat Thukral 2 years, 8 months ago

Hello class 12 inverse trigonometry chapter holds a good amount of weightage but in comparison to other chapters, it is easy to understand and questions can be made easily which again depends on the capability of a student. I would say if you can give a week including practice this chapter will be done

0Thank You

ANSWER

All characters of ch 4 Anne Frank

Posted by Kajal Soni 2 years, 8 months ago

CBSE > Class 10 > English Language and Literature

0 answers

ANSWER

Write a short note on legislature executive and judiciary

Posted by Aviral Yadav 2 years, 8 months ago

CBSE > Class 10 > Social Science

0 answers

ANSWER

Statement sums

Posted by Asfiya Amani 6A 2 years, 8 months ago

CBSE > Class 05 > Mathematics

1 answers

Asfiya Amani 6A 2 years, 7 months ago

Addition

1Thank You

ANSWER

What is the distance between 0 and 1 called on the numberline?

Posted by Radhika Agarwal 2 years, 8 months ago

CBSE > Class 06 > Maths (OLD)

0 answers

ANSWER

what is electoral college?

Posted by Sweety Sinha 2 years, 8 months ago

CBSE > Class 10 > Social Science

1 answers

Muskan Saha 2 years, 8 months ago

A body of people representing the state of the USA who formally cast word for the election of the President and vice President

1Thank You

ANSWER

How is a star different from a planet?

Posted by Radhika Agarwal 2 years, 8 months ago

CBSE > Class 06 > Social (OLD)

4 answers

Shruti Kakati 2 years, 6 months ago

The star has its own heat and light. It doesn't revolve around the sun The planets shines due to sun's light. The revolve around the sun.

0Thank You

٨🅢🅤🅡🅨🅐 🅜🅘🅢🅡🅐 ×ᴗ× 2 years, 7 months ago

A star has is own heat and light and the planet does not have his own heat and light

2Thank You

Account Deleted 2 years, 8 months ago

Star is heat

0Thank You

Dhru Dhruvil 2 years, 8 months ago

0Thank You

ANSWER

Who is the biggest fandom in the world

Posted by Anjali Anjali 2 years, 8 months ago

CBSE > Class 07 > Other Subjects

5 answers

Sakshi Dagar 1 year, 11 months ago

BTS

0Thank You

Sakshi Dagar 1 year, 11 months 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.

0Thank You

Kamna Badhan 2 years, 7 months ago

BTS , Harry Potter, the god of rings

0Thank You

Shikha R Praveen Praveen 2 years, 8 months ago

Georphy

1Thank You

Shikha R Praveen Praveen 2 years, 8 months ago

bts

2Thank You

ANSWER