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Simplify the following to a rational num...

Simplify the following to a rational number `([4+sqrt(15)]^(3//2)+[4-sqrt(15)]^(3//2))/([6+sqrt((35))]^(3//2)-[6-sqrt((35))]^(3//2))`

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ML KHANNA-LOGARITHMS AND SURDS-Problem Set (4)
  1. Show that the expression sqrt(2)[2x+sqrt((x^(2)-y^(2)))][sqrt(x-sqrt((...

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

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

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  4. Simplify (a) sqrt(9-6a+a^(2))+sqrt(9+6a+a^(2)) if a lt -3. (b) (1)...

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  5. Show that (sqrt(7))/(sqrt([16+6sqrt((7))])-sqrt([16-6sqrt((7))])) is a...

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  6. Express (4+3sqrt(3))/([7+4sqrt((3))]) in the form A+sqrt(B), where A a...

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  7. Evaluate (97+56sqrt(3))^(1//4).

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  8. Given sqrt(5)=2.23607, find the value of (10sqrt(2))/(sqrt((18))-sqrt...

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  9. If ax=(2pq)/(1+q^(2)), find the value of (sqrt((p//a)+x)+sqrt((p//a)-x...

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  10. If x=a((m^(2)+n^(2))/(2mn))^(1//2) , a, m, n gt 0, m gt n, find the va...

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  11. If x=(sqrt(7)-sqrt(5))/(sqrt((7))+sqrt((5))), y=(sqrt(7)+sqrt(5))/(sqr...

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  12. If sqrt(3)=1.732, find the value of (sqrt(26-15sqrt((3))))/(5sqrt((2))...

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  13. Find the square root of : 21-4sqrt(5)+8sqrt(3)-4sqrt(15).

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  14. Find the square root of : 5-sqrt(10)-sqrt(15)+sqrt(6).

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  15. Square root of 6 + sqrt(12) - sqrt(24) - sqrt(8) is

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  16. Find the square root of : 21+3sqrt(8)-6sqrt(3)-6sqrt(7)-sqrt(24)-sqrt(...

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  17. The value of sqrt(6+2sqrt(3)+2sqrt(2)+2sqrt(6))-(1)/(sqrt(5-2sqrt(6)))...

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  18. Prove that sqrt(10+sqrt((24))+sqrt((40))+sqrt((60)))=sqrt(2)+sqrt(3)+s...

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  19. Without extracting the roots, determine which is greater sqrt(11)-sqrt...

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  20. Prove that for x ge 1, the expression sqrt(x+2sqrt((x-1)))+sqrt(x-2sqr...

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