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Supp0se √2 is rational.
Then √2 can be written as a fraction of integers in its simplest form.
So √2 = a/b , where a,b are integers, b is not equal to 0 and a, b are coprimes.
Squaring both sides we get
2=a^2/b^2
Then a^2 = 2×b^2 ......(1)
So 2 is a factor of a^2.
Since 2 is prime 2 is a factor of a ......(2)
So a = 2m for some integer m. Substitute this in (1),
4m^2 = 2b^2
=> 2m^2 = b^2
=> 2 is a factor of b^2
So 2 is a factor of b. ...(3)
From (2) and (3) 2 is a common factor of a and b.
Which is a contradiction to the fact that a and b are coprimes.
So our assumptio that √2 is rational is wrong .
So √2 is irrational.

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ANSWER

prove that[ 3 plus 2root 5 ]square is an irrational no

Posted by Navjot Kaur 7 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Susai Raj 7 years, 6 months ago

We know that the sum of a rational and an irrational is irrational and the product of a rational and an irrational is irrational and √5 is irrational.
So (3+2√5)^2
=3^2+2×3×2√5+(2√5)^2
=9+12√5+20
=29+12√5
Here 12√5 is irrational and hence 29+12√5 is irrational.

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Solve the equation x + y = a + b.and ax + by= a^2 _b^2.

Posted by Rakesh Rajbhar 7 years, 6 months ago

CBSE > Class 10 > Mathematics

0 answers

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Euclid division method 121121 and 121

Posted by Priyanshu Nagar 7 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Priyanshu Nagar 7 years, 6 months ago

H. C. F 121

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What is coordinate geometry

Posted by Hritik Singh 7 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Kirtan Patel 7 years, 6 months ago

A geometry dealing with plane figure divided into 4 quadrants having two perpendicular lines namely x and y axis

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3x square -6x +2

Posted by Sumit Mishra 7 years, 6 months ago

CBSE > Class 10 > Mathematics

0 answers

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SinA sin(90-A)-cosAcos(90-A)

Posted by Adarsh Kanungo 7 years, 6 months ago

CBSE > Class 10 > Mathematics

2 answers

Ankita ?? Arpita☺️ 7 years, 6 months ago

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Krituk Nikhra 7 years, 6 months ago

SinA sin(90-A)- cosA cos)90_A) =SinA cosA-cosA sinA = 0

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Show that the cube of any positive integer is of the form 4m+1 or4m+3 for some integer

Posted by Abhiraj Jain 7 years, 6 months ago

CBSE > Class 10 > Mathematics

0 answers

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Prove under root 2 and under root 3 are irrational numbers

Posted by Prachi Nagar 7 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Priyanshu Nagar 7 years, 6 months ago

under root 3 is equal to a upon B और a and b are co prime under root 3 is equal to a upon B =3= ए स्क्वायर upon बी स्क्वायर=3b square = a square = 3 Mod a square =3 mod a = a=c for some integer c = a square = 9c square = 3b square = 9c square =b square =3c square =3mod b square =3mod b From 1and2 we observe that a and b have at least 3as comman factor. But this contraDicts the fact that a and b are coprime. This means that our assumption is not correct. Hence under root 3 is an irrational number

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Posted by Khushi Manuja 5 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Sarthak Gupta 7 years, 6 months ago

What the question Khushi manuja

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Prove that 2√3 +√5 is irrational number.Also, check whether (2√3+√5) ×(2√3-√5) is rational or irrational

Posted by Khushi Manuja 7 years, 6 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

Pythagoras theorum

Posted by Sahil Punjabi 7 years, 6 months ago

CBSE > Class 10 > Mathematics

2 answers

Ankita ?? Arpita☺️ 7 years, 6 months ago

H^2=p^2+b^2

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Varun Srivastav 7 years, 6 months ago

Phythagoras theroem states that (Hypotenuse)sq=(Perpendiculal)sq+(base)sq ::::Sq is square::::

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If sec theta + tan theta is equals to p so that p square minus 1 divided by p square + 1 is equals to sin theta

Posted by Niranjan Shastri 7 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Ankita ?? Arpita☺️ 7 years, 6 months ago

Then what ????

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Understanding graphical method of solving simultaneous linear equation

Posted by Nihar Dash 7 years, 6 months ago

CBSE > Class 10 > Mathematics

0 answers

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Prove that sin (theta) - cos (theta)+1/sin (theta)+cos (theta)-1 equals to 1/sec(theta)-tan(theta)

Posted by Abhijeet Singh Gaur 7 years, 6 months ago

CBSE > Class 10 > Mathematics

0 answers

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Find the value of 2x

Posted by Rohit Kumar 7 years, 6 months ago

CBSE > Class 10 > Mathematics

2 answers

Varun Srivastav 7 years, 6 months ago

Write complete question Raushan??

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Divanshu Rawat 7 years, 6 months ago

In what condition ??????

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For what value of k,k-3,2k+1,4k+3 are in A.P

Posted by Lakshya Khandelwal 7 years, 6 months ago

CBSE > Class 10 > Mathematics

0 answers

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Solve for X and y : 2/x+3/y=2,1/x-1/2y=1/3

Posted by Mrudul Manwatkar 7 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Divanshu Rawat 7 years, 6 months ago

X =0 ,Y=3/2

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If sinA=a2-b2/a2+b2 find cos A and tanA

Posted by Abhishek Kumar 7 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Lucky Arya 7 years, 6 months ago

Cos A= 2ab/a2+b2. , TanA = a2-b2/2ab

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Give two different examples of pair of similar figures and non - similar figures

Posted by Srinidhi Srinivasulu 7 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Srinidhi Srinivasulu 7 years, 6 months ago

Two different examples of a pair of (i) Similar figures : (a) Any 2 rectangles (b) Any 2 square (ii) Non - Similar figures : (a) A scalene and an equilateral triangle. (b) An equilateral triangle and a right angled triangle

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If Alfa,beta are zeroes of quadratic polynomial no-go(k+6)x+2(2k-1)find k if Alfa+beta=1/2

Posted by Sanjana Bisht 7 years, 6 months ago

CBSE > Class 10 > Mathematics