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Rationalize the denominator and simplify...

Rationalize the denominator and simplify:
` (2sqrt6-sqrt5)/( 3sqrt5-2sqrt6) `

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The correct Answer is:
` (9+ 4 sqrt(30))/(21)`
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KUMAR PRAKASHAN-NUMBER SYSTEMS-Skill Testing Exercise
  1. Rationalize the denominator and simplify: (sqrt3-sqrt2)/( sqrt3+sq...

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  2. Rationalize the denominator and simplify: (4sqrt3+5sqrt2)/( 4sqrt3...

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  3. Rationalize the denominator and simplify: (2sqrt6-sqrt5)/( 3sqrt5-...

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  4. If the x= 8+ 3sqrt7 , find the value of x^(2) + (1)/(x^(2)) .

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  5. If the x= 5 +2sqrt6 find the value of x^(2) + (1)/(x^(2)) and x^(3)...

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  6. If p= (sqrt3- sqrt2) /( sqrt3+ sqrt2) and q= (sqrt3+sqrt2)/( sqrt3- sq...

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  7. If x= 2 +sqrt3. find the value of x^(3) +(1)/(x^(3))

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  8. If x = 4 +sqrt(15) . Find the value of x^(2) +(1)/(x^(2)) and x^(3...

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  9. Simplify : (3sqrt2-2sqrt3)/( 3sqrt2+2sqrt3) +(sqrt(12))/( sqrt3- s...

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  10. Simplify : (2)/(sqrt5+ sqrt3) + (1)/(sqrt3+sqrt2) - (3)/(sqrt5+sqr...

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  11. Simplify (sqrt5-2)/( sqrt5+2) - (sqrt 5+2)/( sqrt5-2)

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  12. Simplify : (5+sqrt3)/(7- 4sqrt3) -(5-sqrt3)/( 7+4sqrt3)

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  13. If a + 8 sqrt5 b = ( 8+ sqrt5)/( 8- sqrt5) , find a and b ,

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  14. Find the values of a and b . If (2sqrt6-sqrt5)/( 3sqrt5-2sqrt6)=...

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  15. Find a and b , if (4+ sqrt2)/( 2+sqrt2) = a- bsqrtb.

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  16. Find a and b . If (4+ sqrt5)/( 2+sqrt5) = a+bsqrt5.

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  17. Represent sqrt(5) on the number line.

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  18. If x= 5 and y=2 find the values of : (x^(y)+ y^(x) )

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  19. If x= 5 and y=2 find the values of : (x^(x) + y^(y)) ^(-1)

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  20. Simplify : [ 5^(2) (8^((1)/(3)) +27^((1)/(3)) )^(3) ]^((1)/(5))

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