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It being given that sqrt(3) = 1.732, sq...

It being given that `sqrt(3) = 1.732, sqrt(5) = 2.236, sqrt(6) = 2.449` and `sqrt(10) = 3.162`, find to three places of decimal, the value of the following .
(i) `(1)/(sqrt(6) + sqrt(5))` (ii) `(6)/(sqrt(5) + sqrt(3))` (iii) `(1)/(4sqrt(3) - 3sqrt(5))`
(iv) `(3 + sqrt(5))/(3-sqrt(5))` (v) `(1+2sqrt(3))/(2-sqrt(3))` (vi) `(sqrt(5) + sqrt(2))/(sqrt(5) - sqrt(2))`

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Verified by Experts

The correct Answer is:
(i) 0.213 (ii) `2sqrt(2)` (iii) 4.545 (iv) 6.854 (v) 16.660 (vi) 4.441
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It being given that sqrt(2) = 1.414, sqrt(3) = 1.732, sqrt(5) = 2.236 and sqrt(10)= 3.162 , find the value to three places of decimials, of each of the following . (i) (2)/(sqrt(5)) (ii) (2- sqrt(3))/(sqrt(3)) (iii) (sqrt(10) - sqrt(5))/(sqrt(2))

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

(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))

Simplify (i) (3-sqrt(11))(3+sqrt(11)) (ii) (-3+ sqrt(5))(-3-sqrt(3)-sqrt(5)) (iii) (3- sqrt(3))^(2) (iv) (sqrt(5) - sqrt(3))^(2) (v) (5+ sqrt(7))(2+ sqrt(5)) (vi) (sqrt(5) - sqrt(2))(sqrt(2) - sqrt(3))

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

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

Simplify: (2)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+sqrt(2))-(3)/(sqrt(5)+sqrt(2))

(iii) simplify (2)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+sqrt(2))-(3)/(sqrt(5)+sqrt(2))

Simplify ((sqrt(5)-sqrt(3))(sqrt(5)+sqrt(3)))/((sqrt(5)+2)+(2-sqrt(5)))

RS AGGARWAL-NUMBER SYSTEMS-Exercise 1F
  1. It being given that sqrt(2) = 1.414, sqrt(3) = 1.732, sqrt(5) = 2.23...

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  2. Find rational numbers a and b such that .

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  3. It being given that sqrt(3) = 1.732, sqrt(5) = 2.236, sqrt(6) = 2.449...

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  4. Simplify by raationalising the denominator. (i) (7sqrt(3) - 5sqrt(2...

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  5. Simplify (2+ sqrt(3))/(2-sqrt(3))+(2-sqrt(3))/(2+sqrt(3))

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  6. Prove that (i) (1)/(3+sqrt(7)) + (1)/(sqrt(7)+sqrt(5))+(1)/(sqrt(5)+...

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  7. Find the value of a and b if (7+3sqrt(5))/(3+sqrt(5))-(7-3sqrt(5))/...

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  8. Simplify (sqrt(13)-sqrt(11))/(sqrt(13)+sqrt(11)) + (sqrt(13)+sqrt(11))...

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  9. If x=3+2sqrt(2), check whether x+1/x is rational or irrational.

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  10. if x=2-sqrt(3), find the value of (x-1/x)^3

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  11. If x = 9 - 4sqrt(5), find the value of x^(2) +(1)/(x^(2)).

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  12. If x = (5-sqrt(21))/2, find the value of x+(1)/(x)

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  13. If a=3-2sqrt2, find the value of a^2-1/a^2.

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  14. If x = sqrt(13)+2sqrt(3), find the value of x-(1)/(x) .

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

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  16. If x = (5-sqrt(3))/(5+sqrt(3)) and y = (5+sqrt(3))/(5-sqrt(3)), show ...

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  17. If a= (sqrt(5) + sqrt(2))/(sqrt(5) -sqrt(2)) and b = (sqrt(5)-sqrt(2))...

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  18. If a=(sqrt3-sqrt2)/(sqrt3+sqrt2) and b=(sqrt3+sqrt2)/(sqrt3-sqrt2) the...

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  19. If p = (3-sqrt(5))/(3+sqrt(5)) and q = (3+sqrt5)/(3-sqrt(5)),find the...

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  20. Rationalise the denominator of each of the following. (i) (1)/(sqr...

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