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Prove that root 2 + root 5 is an irrational number

Posted by Amishi Agarwal 2 years, 8 months ago

1 answers

Muskaan Syed 2 years, 8 months ago

Let's assume that √2 + √5 is a rational number. √2+√5=a/b Sq. On both sides =2+5+2√10= a^2/b^2 2√10=a^2/b^2 -7 2√10=a^2-7/b^2. √10=a^2-7/2b^2 . It's a fact that √10 is irrational. Hence our assumption that √2+√5 is rational is incorrect..... Hence, √2+√5 is irrational

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To prove root 2 is irrational

Posted by Amishi Agarwal 2 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

B 01 Rojalin Behera 2 years, 8 months ago

Let assume that √2 is rational So, √2=a/b (a and b are positive co-prime number and b is not equal to 0) i.e. HCF (a,b)=1 b√2=a Squaring both the sides, we get (b√2)^2=a^2 =2b^2=a^2....(i) =b^2=a^2/2 =a^2/2 (if P is a prime number, if P divides a^2 then P divides a) =a/2 So, a=3c for some integer c Putting a=2c in equation (i) 2b^2=(2c)^2 =2b^2=4c^2 =b^2=2c^2 =b^2/2=c^2 =b^2/2 (If P is a prime number, if P divides a^2 then P divides a) =b/2 So, a and b have another prime factor 2 But this contradicts the fact that a and b are co-prime number. This contradiction has arisen due to our incorrect assumption. So, √2 is an irrational number. Hence, proved.

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How did nationalism dovelop culture in Europe? Explain

Posted by Ronaldo Barik 2 years, 8 months ago

CBSE > Class 10 > Social Science

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find out more About nationalist symbols in countries outside europe .for one or two countries collect examples of pictures posters or music thar are symbols of nationalism .how are these different from european Examples

Posted by Bharath Kumar 2 years, 8 months ago

CBSE > Class 10 > Social Science

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Swachhata ke prati jagrukta failane ke liye Sarkar ki or se vigyapan likhiye

Posted by Laksh Rana 2 years, 8 months ago

CBSE > Class 10 > हिंदी ब

0 answers

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What is an image and it's properties

Posted by Vansh Sen 2 years, 8 months ago

CBSE > Class 10 > Science

0 answers

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Speech on rule Liberty is freedom from poverty deprivation and all forms of discrimination

Posted by Sastika Dharani 2 years, 8 months ago

CBSE > Class 10 > English Language and Literature

0 answers

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2cos 30-1

Posted by Cccc Bbb 2 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Sourav Singh 2 years, 8 months ago

-0.133974596

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If alpha and beta are the zeroes of polynomial ax²+bx+c, find the value of alpha²+beta²

Posted by Paridhi Saxena 2 years, 8 months ago

CBSE > Class 10 > Mathematics

3 answers

Sourav Singh 2 years, 8 months ago

α2+β2=a2b2−2ac

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Ashish Ashish 2 years, 8 months ago

Paper to easy hota hai ya hard

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Ashish Ashish 2 years, 8 months ago

Sir mai 10th compartment kar rha hu

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Describe the destruction caused by hailstrom in lencho's field?

Posted by Shruti Patel 2 years, 8 months ago

CBSE > Class 10 > English Language and Literature

1 answers

Muskan Saha 2 years, 8 months ago

The destruction caused by the hailstorm on lencho filled was devasting. The hailstorm rain on the value for several hours and lencho's field was completed destroyed.

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In the chapter," two gentlemen of Verona" what struck one most was the willingness of the boys to work" talking clue from the above quoted lines, write an article on " earning livelihood with dignity of labour "

Posted by P Niyathi 2 years, 8 months ago

CBSE > Class 10 > English Language and Literature

1 answers

P Niyathi 2 years, 8 months ago

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What is heterotorphic

Posted by Harish Kumar 2 years, 8 months ago

CBSE > Class 10 > Science

5 answers

Niraj Kumar 2 years, 8 months ago

Organisms which depend on other organism for their food and it does not have ability to prepare their own food

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Srijoy Roy 2 years, 8 months ago

Organisms which depend directly or indirectly on other organisms for their food

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Ansh Yadav 2 years, 8 months ago

Organisms which depand on other organisms for their food

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Suman Jha 2 years, 8 months ago

Heterotrophic are those who depend on other organism they can't make their own food

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Muskan Saha 2 years, 8 months ago

The plants that cannot make their food by using photosynthesis process.they depend on other living organisms.

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As office manager, Spring Meadow’s School, Nasik, place an order for stationery including A – 4 size paper, DeskJet ink cartridge, refills (red and blue), chart paper, and boxes of chalk. Write a letter to Khanna Brothers, Stationers, Nasik, giving the details in not more than 150 words regarding the mode of dispatch and the mode of payment in not more than 150 words.

Posted by Rutuja Londhe 2 years, 8 months ago

CBSE > Class 10 > English Language and Literature

0 answers

ANSWER

Draw a mind map on Nelson Mandela

Posted by Namita Dahiya 2 years, 8 months ago

CBSE > Class 10 > English Language and Literature

0 answers

ANSWER

How much energy is transferred during 5minutes when a current of 3A flows through a 9V electrical device?

Posted by Varshika Ganesh Babu 2 years, 8 months ago

CBSE > Class 10 > Science

0 answers

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In a school there are two sections A and B of class X . There are 48 students in section A and 60 students in section B. Determine the least number of books required for the library of school so that the books can be distributed equally among all students of each section?

Posted by Kaushik Krishna 2 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Aditya D 2 years, 8 months ago

LCM of 48 and 60 = 240 bookd

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Reading comprehension on rapid transition of online learning as a result of covid19

Posted by Arpan Choudhary 2 years, 8 months ago

CBSE > Class 10 > English Language and Literature

0 answers

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how to transport oxygen and carbon dioxide in human being

Posted by Shivam Singh 2 years, 8 months ago

CBSE > Class 10 > Science

1 answers

Muskan Saha 2 years, 8 months ago

Hemoglobin present in blood aids in the transportation of this gases the blood serve as a transfer system for both carbon dioxide and oxygen is carried to the cell where is carbon dioxide is carried away from the cells...

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What is the balanced equatiion of Al 2 O 3 ____ Al+O2

Posted by Dhiman Sandialya 2 years, 8 months ago

CBSE > Class 10 > Science

2 answers

Sravya Sudhagoni 2 years, 8 months ago

2Al2O3 ---------4Al+3O2

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B 01 Rojalin Behera 2 years, 8 months ago

2Al2O3_____4Al+3O2

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Find the zeros of the polynomial x⁴-2x²+3x³+5x-2÷x+2

Posted by Mohammed Ali Rahib 2 years, 8 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

Why it is necessary to balance a equation?

Posted by Manya Malik 2 years, 8 months ago

CBSE > Class 10 > Science

5 answers

Ananya Jha 2 years, 8 months ago

It is necessary to balance an equation in order to follow the law of conservation of mass which says that mass can neither be created nor be destroyed in a chemical reaction it can only change its state... The sum total of both the masses(LHS and RHS)are equal before and after the reaction.

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Ansh Yadav 2 years, 8 months ago

Because of law of conservation of mass

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Suman Jha 2 years, 8 months ago

Due to law of conservation of mass which states that mass can neither be created nor be destroyed in a chemical reaction that's why it is necessary to balance a chemical equation

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Ayush Mohanty 2 years, 8 months ago

In order not to violate the law of conservation of mass..

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Aspirant Aspirant 2 years, 8 months ago

It is necessary to balance a equation to follow law of conservation of mass. That says that mass can neither be created nor be destroyed in a chemical reaction.

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Explain the qualities of post office employees

Posted by Urvi Tembhare 2 years, 8 months ago

CBSE > Class 10 > English Language and Literature