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Prove the following identities. ((a+2)...

Prove the following identities.
`((a+2)^(2)(a-3)+(a^(2)-4)sqrt(a^(2)-9))/((a-2)^(2)(a+3)+(a^(2)-4)sqrt((a^(2)-9)))=((a+2)sqrt(a-3))/((a-2)sqrt((a+3)))` `(a ge 3)`.

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ML KHANNA-LOGARITHMS AND SURDS-Problem Set (4)
  1. Express as an equivalent fraction with rational denominator. ([sqrt(...

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  2. (12)/( 3+ sqrt(5 ) + 2sqrt(2)) is equal to

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  3. Prove the following identities. ((a+2)^(2)(a-3)+(a^(2)-4)sqrt(a^(2)-...

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  4. Prove the following identities. (n^(3)-3n+(n^(2)-1)sqrt(n^(2)-4)-2)/...

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  5. Express with rational denominator : (4)/(root3((9))-root3(3)+1)

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  6. Express with rational denominator : (sqrt(8)+root3(4))/(sqrt((8))-ro...

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  7. Find the square root of (A) 8+2sqrt(15), (B)49+20sqrt(6)

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  8. Find the square root of (A) 6-sqrt(35) (B) 5sqrt(6)+12.

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  9. Find the square root of sqrt(27)+sqrt(15).

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  10. Find the square root of sqrt(18)-sqrt(16).

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  11. Find the square root of sqrt(32)-sqrt(24).

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  12. Find the square root of (i) (2+sqrt(3))/(2), (ii) 12-sqrt(68+48sqrt(...

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  13. Find the square root of 2x-1+2sqrt(x^(2)-x-6).

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  14. Find the square root of a+x+sqrt(2ax+x^(2)).

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  15. Find the square root of (i) (3//2)(x-1)+sqrt(2x^(2)-7x-4) (ii) 1-x...

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  16. Find the square root of 1+a^(2)+sqrt(1+a^(2)+a^(4))

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  17. Find the square root of x+y+z+2sqrt(xz+yz).

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  18. Show that the expression sqrt(2)[2x+sqrt((x^(2)-y^(2)))][sqrt(x-sqrt((...

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  19. Show that the square to (sqrt(26-15))//(5sqrt(2)-sqrt(38-5sqrt(3))) is...

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  20. Simplify the following to a rational number ([4+sqrt(15)]^(3//2)+[4-sq...

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