Question

rench questions
29. Prove that √2 + 3√5is an irrational number.
Also check whether (√2+3√5) (√2-3√5)
is rational or irrational
(or)
A rectangular park is to be designed whole breadth is 3m less than its length. Its area is
to be 4 square meters more than the area of park, that has already been made in the
shape of isosceles triangles with its base as the breadth of the rectangular park and
altitude 12. Find the length and breadth.
30. Three metallic spheres of radii 6 cm, 8cm and 10cm respectively are melted together to
form a single salid sphere. Find the radius of the resulting sphere.
(or)​

Answer 1

Answer:

let us assume 2√3+√5 as rational.

we can get integers a&b in the form a/b.

2√3+√5=a/b

squaring obs  

i dont know about this questions answer

A rectangular park is to be designed whole breadth is 3m less than its length. Its area is

to be 4 square meters more than the area of park, that has already been made in the

shape of isosceles triangles with its base as the breadth of the rectangular park and

altitude 12. Find the length and breadth.

30. Three metallic spheres of radii 6 cm, 8cm and 10cm respectively are melted together to

form a single salid sphere. Find the radius of the resulting sphere.

(2√3+√5)sq= (a/b)sq

(2√3)sq +(√5)sq+2(2√3×√5)= (a)sq/(b)sq

20+5+4+2√15=(a)sq/(b)sq 2√15=(a)sq/(b)sq - 29

since a&b are integers 2√15 is rational

but this contradicts that 2√3+√5 is irrational.

this contradiction has arisen due to the incorrect assumption that 2√3+√5 is rational .

hence it is irrational.