[" - "[" 3.सिद्ध कीजिए कि निम्नलिखत संख्याएँ अपरिमेय हैं: "],[" (i) "(1)/(sqrt(2))," (ii) "7sqrt(5)]]

Expand: (i) (sqrt 3 + sqrt 2)^4 (ii) (sqrt 5 - sqrt 2)^5

Simplify : (i) (5+sqrt(5))(5-sqrt(5)) (ii) (3+2sqrt(2))(3-2sqrt(2))

12.Rationalise and find the value of' "a'" and "'b'" ; (i) "(sqrt(3)-1)/(sqrt(3)+1)=a+b sqrt(3), (ii) (sqrt(5)-2)/(sqrt(5)+2)=a+b sqrt(5)

Rationalize the denominator of : (i) (2sqrt(3))/sqrt(5)" (ii) "1/(sqrt(3)-sqrt(2))

Simplify : (sqrt5+7i)(sqrt5-7i)^3 .

सिद्ध कीजिए कि |vecA xx vecB|^(2) + |vecA * vecB|^(2) = (AB)^(2).

Find the reciprocal of : (i) 7+sqrt(7)i (ii) i-5 .

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

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))

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))