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Evaluate : (1)/(3-sqrt(8)) -(1)/(sqrt(8)...

Evaluate : `(1)/(3-sqrt(8)) -(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2).`

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Let T = (1)/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7)) +(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)+2) then-

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Show that: 1/(3-sqrt(8))-1/(sqrt(8)-sqrt(7))+1/(sqrt(7)-sqrt(6))-1/(sqrt(6)-sqrt(5))+1/(sqrt(5)-2)=5

Prove that: 1/(3-sqrt(8))-1/(sqrt(8)-\ sqrt(7))+1/(sqrt(7)-\ sqrt(6))-1/(sqrt(6)-\ sqrt(5))+1/(sqrt(5)-2)=5

1/(sqrt(7)+sqrt(3))\times (sqrt(7)-sqrt(3))/(sqrt(7)-sqrt(3))

(1)/(2sqrt(5)-sqrt(3))-(2sqrt(5)+sqrt(3))/(2sqrt(5)+sqrt(3)) =

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Simplify : (1)/(sqrt(3)+sqrt(2))-(1)/(sqrt(3)-sqrt(2))+(2)/(sqrt(2)+1)

Prove that (1)/(sqrt(7))=(1)/(sqrt(7))times(sqrt(7))/(sqrt(7))

The value of log_((9)/(4))((1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3)))))...oo) is

ICSE-RATIONAL AND IRRATIONAL NUMBERS -EXERCISE 1 (D)
  1. Evaluate : (1)/(3-sqrt(8)) -(1)/(sqrt(8)-sqrt(7))+(1)/(sqrt(7)-sqrt(6)...

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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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