Which of `(sqrt15 + sqrt3) and (sqrt10 + sqrt8)` is greater ?

1.	Which of `(sqrt15 + sqrt3) and (sqrt10 + sqrt8)` is greater ?
Answer» We have `(sqrt15 + sqrt3)^(2) = (sqrt15)^(2) + 2 xx sqrt15 xx sqrt3 + (sqrt3)^(2)` `= 15 + 2 sqrt45 + 3 = 18 + 2 xx sqrt45` Again, we have `(sqrt10 + sqrt8)^(2) = (sqrt10)^(2) + 2 xx sqrt10 xx sqrt8 + (sqrt8)^(2)` `= 15 + 2 sqrt45 + 3 = 18 + 2 xx sqrt45` Again, we have `(sqrt10 + sqrt8)^(2) = (sqrt10)^(2) + 2 xx sqrt10 xx sqrt8 + (sqrt8)^(2)` `= 10 + 2 xx sqrt(10 xx 8) + 8` `= 18 + 2 sqrt80` Now, `sqrt80 gt sqrt45 , :. (sqrt10 + sqrt8)^(2) gt (sqrt15 + sqrt3)^(2)` `rArr (sqrt10 + sqrt8) gt (sqrt15 + sqrt3)` Hence between `(sqrt10 + sqrt8) and (sqrt15 + sqrt3), (sqrt10 + sqrt8)` is greater

Discussion

If `x = 2 + sqrt3, y = 2 - sqrt3`, then find the simpliest value of (a) `x - (1)/(x)`, (b) `y^(2) + (1)/(y^(2))`, (c) `x^(3) - (1)/(x^(3))`, (d) `xy + (1)/(xy)`
If `m + (1)/(m) = sqrt3`, then find the simpliest value of (i) `m^(2) + (1)/(m^(2))` and (ii) `m^(3) + (1)/(m^(3))`:
The simpliest value of `(sqrt5 (sqrt(3 - sqrt5)))/(sqrt2 + sqrt(7 - 3 sqrt5))` isA. 1B. 5C. 10D. None of these
Rationalise the denominator: (a) `(1)/(root(3)(3) + root(3)(2))`, (b) `(2)/(sqrt5 + sqrt3 + sqrt2)`, (c) `(x^(2))/(sqrt(x^(2) + y^(2)) - y)`, (d) `(1)/(sqrt6 + sqrt5 - sqrt11)` (e) `(sqrt(x + 2y) - sqrt(x -2y))/(sqrt(x + 2y) + sqrt(x - 2y))`, (f) `(sqrt10 + sqrt5 - sqrt3)/(sqrt10 - sqrt5 + sqrt3)`
Prove that `(12)/(3 + sqrt5 - 2 sqrt2) = 1 + sqrt5 + sqrt10 - sqrt2`
`sqrt7 - sqrt5` is a binomial surd
Which of `(sqrt15 + sqrt3) and (sqrt10 + sqrt8)` is greater ?
Between `(sqrt6 + sqrt7) and (sqrt5 + sqrt8)`, the greater one is-A. `sqrt5 + sqrt8`B. `sqrt6 + sqrt7`C. `sqrt5 + 2 sqrt2`D. None of these
Which one is greater between `(sqrt7 - sqrt5) and (sqrt13 - sqrt11)` ?
Express in the form of like surds: `root(3)(4), root(6)(5), 2sqrt3`.