Prove that:
`sqrt {a/b}=sqrt a/sqrt b`

Prove that: 2^((sqrt((log)_a4sqrt(a b)+(log)_b4sqrt(a b))-sqrt((log)_a4sqrt(b/a)+(log)_b4sqrt(a/b))))dotsqrt((log)_a b)={2ifbgeqa >1 and 2^(log_a(b) if 1

If alpha,beta are the roots of the equation ax^(2)-bx+b=0 , prove that sqrt((alpha)/(beta))+sqrt((beta)/(alpha))-sqrt((b)/(a))=0 .

If in a triangle ABC, (tanA)/1= (tanB)/2 = (tanC)/3 then prove that 6sqrt(2a)=3sqrt(5b)=2sqrt(10)c

Prove that sqrt(3)+\ sqrt(5) is an irrational number.

Prove that sqrt3+sqrt5 is irrational

In any triangleABC , prove that (sqrt(sinA)-sqrt(sinB))/(sqrt(sinA) + sqrt(sinB)) = (a+b-2sqrt(ab))/(a-b) [Hint : (a-b)^(2) = a^(2)+b^(2)-2ab ]

The arithmetic mean between a and b is twice the geometric mean between a and b. Prove that : (a)/(b) = 7+ 4sqrt3 or 7- 4sqrt3

Prove that sqrt(3)+sqrt(4) is an irrational number.

Prove that sqrt(3)+sqrt(5) is irrational.

Prove that sqrt(2)+sqrt(5) is irrational.