Home
Class 12
MATHS
Show that the square to (sqrt(26-15))//(...

Show that the square to `(sqrt(26-15))//(5sqrt(2)-sqrt(38-5sqrt(3)))` is a rational number.

Text Solution

Verified by Experts

The correct Answer is:
`3`
`5sqrt(2) - sqrt(38 + 5sqrt(3)) = 5sqrt(2) - (1)/(sqrt(2)) sqrt(76 + 2 sqrt(75))`
`= 5sqrt(2) - (1)/(sqrt(2)) -(sqrt(75) + 1) = (sqrt(3)(3sqrt(3) - 5))/(sqrt(2))`
`:. (sqrt(26 - 15sqrt(3)))/(5sqrt(2) - sqrt(38 + 5 sqrt(3))) = (sqrt(52 - 30sqrt(3)))/(sqrt(3)(3sqrt(3) - 5))`
`= (3sqrt(3) - 6)/(sqrt(3)(3sqrt(3)-5)) = (1)/(sqrt(3))` so `p = 1 q = 3`
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    RESONANCE|Exercise PART - I MATHEMATICS SEC - 1|14 Videos

  • TEST PAPERS

    RESONANCE|Exercise PART - I MATHEMATICS SEC - 2|1 Videos

  • TEST PAPERS

    RESONANCE|Exercise PART : 1MATHEMATICS|9 Videos

  • TEST PAPER

    RESONANCE|Exercise CHEMISTRY|37 Videos

  • TEST SERIES

    RESONANCE|Exercise MATHEMATICS|131 Videos

Similar Questions

Explore conceptually related problems

Show that the square to (sqrt(26-15sqrt(3)))/(5sqrt(2)-sqrt(38+5sqrt(3))) is a rational number.

Show that (sqrt(7))/(sqrt([16+6sqrt((7))])-sqrt([16-6sqrt((7))])) is a rational number.

Rationalize (sqrt(10))/(sqrt(5)+sqrt(3))

Prove that root(3)(2+sqrt(5))+root(3)(2-sqrt(5)) is a rational number.

Simplest form of ((sqrt(26 - 15sqrt(3)))/(5sqrt2-sqrt(38+5sqrt3)))^2 is

Show that (sqrt(3)+sqrt(5))^(2) is an irrational number .

The value of the expression sqrt(4+sqrt(15))+sqrt(4-sqrt(15))-sqrt(12-4sqrt(5)) is a. An irrational number b.A negative integer c.A natural number d.A non integer rational number

Multiply : (sqrt(3)+sqrt(2)) (5sqrt(2)+sqrt(3))