साबित करें कि निम्नलिखित अपरिमेय हैं: (i) `1/(sqrt(2))` (ii) `7sqrt(5)` (iii) `6+sqrt(2)`...

(iii) (1+i)/(sqrt(2))=sqrt(i)

(ii) log_(sqrt(5)+1)(6+2sqrt(5))

Rationalise the denominators of the following: (i) 1/(sqrt(7)) (ii) 1/(sqrt(7)-sqrt(6)) (iii) 1/(sqrt(5)+sqrt(2)) (iv) 1/(sqrt(7)-2)

Rationalise the denominators of the following : (i) (1)/(sqrt(7)) (ii) (1)/(sqrt(7)-sqrt(6)) (iii) (1)/(sqrt(5)+sqrt(2)) (iv) (1)/(sqrt(7)-2)

Prove that the following are irrationals: ( i ) (1)/(sqrt(2)) (ii) (iii) 6+sqrt(2)

(sqrt(6)+sqrt(5)+ 1/(sqrt(6)+sqrt(5)))^2

Write the following as complex numbers: (i) 1+sqrt(-1) (ii) 4-sqrt(-5) (iii) (sqrt(3))/(2)-(sqrt(-2))/(7)

Rationalise the denominator of each of the following. (i) (1)/(sqrt(7)) (ii) (sqrt(5))/(2sqrt(3)) (iii) (1)/(2+ sqrt(3)) (1)/(sqrt(3)) (v) (1)/((5+3sqrt(2)) (vi) (1)/(sqrt(7) - sqrt(6)) (vi) (1)/(sqrt(7) - sqrt(6)) (viii) (1+ sqrt(2))/(2-sqrt(2)) (ix) (3-2sqrt(2))/(3+2sqrt(2))

sqrt(3i)+sqrt(-3i)=(i)+-2sqrt(3)(ii)+-sqrt(6)(iii)3(iv)3i

Rationalise the denominator of each the of the following : (i)(1)/(3+sqrt(5))" "(ii)(1)/(sqrt(5)-sqrt(3))" "(iii)(16)/(sqrt(41)+5)" "(iv)(30)/(5sqrt(3)+3sqrt(5))" "(v)(3-2sqrt(2))/(3+2sqrt(2))