सिद्ध कीजिए कि निम्नलिखित संख्याएँ अपरिमेय है :
(i) `(1)/(sqrt(2))` (ii) `7sqrt(5)` (iii) `6+sqrt(2)`

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

Prove that the following are irrationals (1) (1)/sqrt(2) (2) 7sqrt(5) (3)6+sqrt(2)

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

Find the square roots of the following: (i) 3-4sqrt(7)i (ii) 4+6sqrt(-5) (iii) -2+2sqrt(3)i .

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)

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))

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 : (i) sqrt(i)= (1+i)/(sqrt(2)) (ii) sqrt(-i)=(1- i)/(sqrt(2)) (iii) sqrt(i)+sqrt(-i)=sqrt(2)

Prove that : (i) sqrt(i)= (1+i)/(sqrt(2)) (ii) sqrt(-i)=(1- i)/(sqrt(2)) (iii) sqrt(i)+sqrt(-i)=sqrt(2)