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Prove that : (1)/(sqrt(2)+1)+ (1)/(sqrt(...

Prove that : `(1)/(sqrt(2)+1)+ (1)/(sqrt(3)+sqrt(2))+ (1)/(2+sqrt(3))=1 `

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ICSE-RATIONAL AND IRRATIONAL NUMBERS -EXERCISE 1 (D)
  1. Prove that : (1)/(sqrt(2)+1)+ (1)/(sqrt(3)+sqrt(2))+ (1)/(2+sqrt(3))=1

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  2. Simplify : sqrt(18)/(5sqrt(18)+3sqrt(72)-2sqrt(162))

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  3. Simplify : (sqrt(x^(2)+y^(2))-y)/(x-sqrt(x^(2)+y^(2)))-:(sqrt(x^(2)+y^...

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  4. Evaluate, Correct to one place to decimal, the expression 5/(sqrt(20)-...

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  5. If x = sqrt(3)- sqrt(2) find the value of x+(1)/(x)

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  6. If x = sqrt(3)- sqrt(2) find the value of x^(2)+ (1)/(x^(2))

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  7. If x = sqrt(3)- sqrt(2) find the value of x^(3)+ (1)/(x^(3))

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  8. If x = sqrt(3)- sqrt(2) find the value of x^(3)+(1)/(x^(3))- 3 (x^(2...

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  9. State true or false: (i) Negative of an irrational number is irratio...

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  10. Draw a line segment of length sqrt(3) cm.

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  11. Draw a line segment of length sqrt(8) cm.

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  12. Solve : (4-sqrt(5))/(4+sqrt(5))+ (2)/(5+sqrt(3))+(4+sqrt(5))/(4-sqrt(5...

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  13. Show that : x^(3)+(1)/(x^(3))=52 , if x =2 + sqrt(3)

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  14. Show that : x^(2)+ (1)/(x^(2)) = 34 , if x =3 +2sqrt(2)

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  15. Show that : (3sqrt(2)-2sqrt(3))/(3sqrt(2)+2sqrt(3))+(2sqrt(3))/(sqr...

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  16. Show that x is irrational if: x^(2)=6

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  17. Show that x is irrational if: x^(2)=0.009

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  18. Show that x is irrational if: x^(2)=27

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  19. Show that x is rational if : x^(2)=16

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  20. Show that x is rational if : x^(2)=0.0004

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  21. Show that x is rational if : x^(2)= 1(7)/(9)

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