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If x=[-(q)/(2)+sqrt((q^(2))/(4)+(p^(3))/...

If `x=[-(q)/(2)+sqrt((q^(2))/(4)+(p^(3))/(27))]^(1//3)+[-(q)/(2)-sqrt((q^(2))/(4)+(p^(3))/(27))]^(1//3)`, prove that `x^(3)+px+q=0`.

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ML KHANNA-LOGARITHMS AND SURDS-Problem Set (4)
  1. If sqrt(3)=1.732, find the value of (sqrt(26-15sqrt((3))))/(5sqrt((2))...

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

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

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

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

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

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

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

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

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  10. Find the cube root of 72 -32sqrt5

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  11. Find the real cube root of 99-70sqrt(2).

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  12. Find the real cube root of 9sqrt(3)+11sqrt(2).

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  13. Find the real cube root of 38sqrt(14)-100sqrt(2).

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  14. If sqrt(3)=1.732, find the value of (26+15sqrt(3))^(2//3)-(26+15sqrt(3...

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  15. Prove (i) root3(20+14sqrt((2)))+root3(20-14sqrt((2)))=4 (ii) {6+sqrt...

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  16. Let u(n)=(1)/(sqrt((5)))[((1+sqrt(5))/(2))^(n)-((1-sqrt(5))/(2))^(n)] ...

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  17. If x=[-(q)/(2)+sqrt((q^(2))/(4)+(p^(3))/(27))]^(1//3)+[-(q)/(2)-sqrt((...

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  18. Prove that root3(2) cannot be expressed in the form p+sqrt(q) where p ...

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  19. Rationalize the denominator of (1)/(sqrt((a))+sqrt((b))+sqrt((c ))+sqr...

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  20. If A/a = B/b = C/c= D/d then prove that sqrt(Aa)+sqrt(Bb)+sqrt(Cc)+sq...

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