`I f(4+sqrt(15))^(3/2)-(4-sqrt(15))^(3/2)=ksqrt(6)`, then `k` is

If (4 + sqrt15)^((3)/(2)) + (4 - sqrt15)^((3)/(2)) =k. sqrt10 , then k = ____

If x=(4+sqrt(15))^(1//3)+(4-sqrt(15))^(1//3) , then show that x^(3)-3x-8=0 .

Simplify the following to a rational number ([4+sqrt(15)]^(3//2)+[4-sqrt(15)]^(3//2))/([6+sqrt((35))]^(3//2)-[6-sqrt((35))]^(3//2))

Express ((4+sqrt15)^(3//2)+(4-sqrt15)^(3//2))/((6+sqrt35)^(3//2)-(6-sqrt35)^(3//2)) in rational form.

For (1)/(asqrt(x)+bsqrt(y)) the rationalising factor is a asqrt(x)-bsqrt(y) . If x=(7sqrt(3))/(sqrt(10)+sqrt(3))-(3sqrt(2))/(sqrt(15)+3sqrt(2))-(2sqrt(5))/(sqrt(6)+sqrt(5)) , then value of x^(4)+x^(2) is

If int_0^1 (dx)/(sqrt(1 + x) - sqrt(x)) =(ksqrt(2))/(3) , then k is :

Distance between line r=i+j+k+lambda(2i+j+4k) and plane rdot(i+2j-k)=3 is (1) 4/(sqrt(6)) (2) 5/(sqrt(6)) (3) 1/(sqrt(6)) (4) 0 (5) 2/(sqrt(6))

Simplify (i) (4+ sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (ii) (1)/(sqrt(3) + sqrt(2)) - (2)/(sqrt(5)-sqrt(3)) -(2)/(sqrt(2) - sqrt(5)) (iii) (2+sqrt(3))/(2-sqrt(3)) + (2-sqrt(3))/(2+sqrt(3)) + (sqrt(3)-1)/(sqrt(3)+1) (iv) (2+sqrt(6))/(sqrt(2)+sqrt(3))+(6sqrt(2))/(sqrt(6)+sqrt(3)) -(8sqrt(3))/(sqrt(6)+sqrt(2))

sqrt(x+3)+sqrt(x+15)<6

(15-2sqrt(566))*(sqrt(7)-2sqrt(2)3)