iii) `sqrt-3sqrt-6`

Which of the following are AP's ? If they form an AP, find the common difference d and write three more terms. (i) 2, 4, 8, 16, . . . (ii) 2,5/2,3,7/2,. . . (iii) -1.2 ,- 3.2 ,- 5.2 ,- 7.2 ,... (iv) -10 ,-6,-2,2.... (v) 3,3+sqrt2,3+2sqrt2,3+3sqrt2,..." " (vi) 0.2,0.22,0.222,0.2222,..." " (vii) 0,-4,-8,-12,..." " (viii) -(1)/(2),-(1)/(2),-(1)/(2),-(1)/(2),..." " (ix) 1,3,9,27,..." " (x) a,2a,3a,4a,..." " (xi) a,a^(2),a^(3),a^(4),..." " (xii) sqrt2,sqrt8,sqrt18,sqrt32,..." " (xiii) sqrt3,sqrt6,sqrt9,sqrt12,..." " (xiv) 1^(2),3^(2),5^(2),7^(2),..." " (xv) 1^(2),5^(2),7^(2),73,...

Ratonalise the denominator in each of the following and hence evalute by taking sqrt2=1.414, sqrt3=1.732 and sqrt(5)= 2.236 upto three places of decimal. (i)4/sqrt3 , (ii) 6/sqrt6 , (iii)(sqrt10-sqrt5)/2 (iv)sqrt2/(2+sqrt2) ,(v) 1/(sqrt3+sqrt2)

The value of sqrt(5+2sqrt(6)) is (a) sqrt(3)-sqrt(2) (b) sqrt(3)+sqrt(2) (c) sqrt(5)+sqrt(6) (d) none of these

Rationlise the denominator and simplify: ( 12sqrt2)/( sqrt3+ sqrt6)

Let k be a real number such that the inequality sqrt(x-3) +sqrt(6 -x) ge k has a solution then the maximum value of k is sqrt3 (2) sqrt6 -sqrt3 (3) sqrt6 (4) sqrt6 +sqrt3

Is the following computation correct? If not give the correct computation : sqrt((-2))sqrt((-3))=sqrt((-2)(-3))=sqrt((-6))

Is the following computation correct? If not give the correct computation: [sqrt((-2))sqrt((-3))]=sqrt((-2)(-3))=sqrt(-6)

If sqrt(2)=1. 414 , and sqrt(3)=1.732 find the value of sqrt(3)+sqrt(6) upto three place of decimals.

Prove that tan 7 (1^(@))/(2) = sqrt2 - sqrt3 -sqrt4 + sqrt6 = (sqrt3 - sqrt2) (sqrt2 -1).

Let p(x) = a_0+a_1x+ a_2x^2+.............+a_n x^n be a non zero polynomial with integer coefficient . if p( sqrt(2) + sqrt(3) + sqrt(6) )=0 , the smallest possible value of n . is