`(5+2sqrt(3))/(7+4sqrt(3))`

In each of the following determine rational number a\ a n d\ b : (i)\ (3+sqrt(2))/(3-sqrt(2))=a+bsqrt(2) (ii)\ (5+3sqrt(3))/(7+4sqrt(3))=a+bsqrt(3)

Rationales the denominator and simplify: (i) (sqrt(3)-\ sqrt(2))/(sqrt(3)\ +\ sqrt(2)) (ii) (5+2\ sqrt(3))/(7+4\ sqrt(3))

Find the value of m and n : if : ( 5+ 2sqrt3)/( 7+ 4sqrt3) = m + n sqrt3

If both a\ a n d\ b are rational numbers, find the values of a\ a n d\ b in each of the following equalities: (5+2\ sqrt(3))/(7+4\ sqrt(3))=a+bsqrt(3)

If both a\ a n d\ b are rational numbers, find the values of a\ a n d\ b in each of the following equalities: (5+2\ sqrt(3))/(7+4\ sqrt(3))=a+bsqrt(3)

Find the values of a and b in each of the following : (a)(5+2sqrt3)/(7+4sqrt(3))=a-6sqrt(3)" "(b)(3-sqrt(5))/(3+2sqrt(5))=asqrt(5)-(19)/(11) (c )(sqrt(2)+sqrt(3))/(3sqrt2-2sqrt(3))=2-bsqrt(6)" "(d)(7+sqrt(5))/(7-sqrt(5))-(7-sqrt(5))/(7+sqrt(5))=a+(7)/(11)sqrt(5b)

Find the value of a and b in each of the following (i)(3+sqrt(2))/(3-sqrt(2))=a+bsqrt(2)" "(ii)(sqrt(2)+1)/(sqrt(2)-1)=a-bsqrt(2)" "(iii)(5+4sqrt(3))/(5-4sqrt(3))=a-bsqrt(3)

(i) If x = (6ab)/(a + b) , find the value of : (x + 3a)/(x - 3a) + (x + 3b)/(x - 3b) . (ii) a = (4sqrt(6))/(sqrt(2) + sqrt(3)) , find the value of : (a + 2sqrt(2))/(a - 2sqrt(2)) + (a + 2sqrt(3))/(a - 2sqrt(3)) .

Which is/are true ? (A) log_(0.2)3lt log_(2)3 (B) log_(sqrt(5))10ltlog _(sqrt(3))11 (C) log_(sqrt(3))10gtlog _(sqrt(5))11 (D) log _((2-sqrt3))(7-4sqrt(3))gtlog_((sqrt(3)-1))(4-2sqrt(3))

Simplify each of the following : (i) 3/(5-sqrt(3))+2/(5+sqrt(3)) (ii) (4+sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (iii) (sqrt(5)-2)/(sqrt(5)+2)-(sqrt(5)+2)/(sqrt(5)-2)