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Show that: (i)27 ^(1/3)X\ 64 ^(1/3)=\ (...

Show that: `(i)27 ^(1/3)X\ 64 ^(1/3)=\ (27X 64) ^(1/3)` `(ii)(64X\ 729 )^(1/3)=\ 64 ^(1/3)X\ 729 ^(1/3)` `(iii) (-125 X\ 216 )^(1/3) = \ -125 ^(1/3) X \ 216 ^(1/3)` `(iv) (-125X-1000)^(1/3)=-125 ^(1/3)X\ -1000^(1/3)`

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Show that : (i) (729)^(1/3)/(1000)^(1/3)= (729/1000)^(1/3) (ii) (-512)^(1/3)/(343)^(1/3)= (-512/343)^(1/3)

Evaluate: (i) 36^(1/3)X\ 384^(1/3)\ \ \ (ii)96^(1/3) \ X\ 144^(1/3) (ii) 100^(1/3)X 270^(1/3)\ (iv) 121^(1/3)X\ 297^(1/3)

Find: (i) 64^(1/2) (ii) 32^(1/5) (iii) 125^(1/3)

The value of 64^(-1/3)\ (64^(1/3)-64^(2/3)), is (a) 1 (b) 1/3 (c) -3 (d) -2

sqrt(2^x(4^x(0. 125)^(1/ x))^(1/3))=4.(2^(1/3))

Find the derivative (i) x^(1//3) (ii) (2)/(x^(3//2)) (iii) 3x^(-1//4)

Simplify: (i) {(1/3)^(-3)-\ (1/2)^(-3)}-:(1/4)^(-3) (ii) (3^2-\ 2^2)x\ (2/3)^(-3) (iii) {(1/2)^(-1)x\ (-4)^(-1)}^(-1) (iv) [{((-1)/4)^2}^(-2)]^(-1) (v) {(2/3)^2}^3x\ (1/3)^(-4)x\ 3^(-1)x\ 6^(-1)

Factorise (i) 1+64x^(3) (ii) a^(3)-2sqrt(2)b^(3)

simplify (i) (1^(3)+2^(3)+3^(3))^(1/2) (ii) (3/5)^(4)(8/5)^(-12)(32/5)^(6) ,(iii) (1/27)^(-2/3) (vi) [((625)^(-1/2)))^(-1/4)]^(2) ,(v) (9^(1/3)xx27^(-1/2))/(3^(1/6)xx3^(-2/3)) (vi) 64^(-1/3)[64^(1/3)-64^(2/3)] (8^(1/3)xx16^(1/3))/(32^(-1/3)

If x^(-2)=64 , then x^(1/3)+\ x^0= (a) 2 (b) 3 (c) 3/2 (d) 2/3

RD SHARMA ENGLISH-CUBES AND CUBE ROOTS-All Questions
  1. The volume of a cubical box is 32.768 cubic metres. Find the length...

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  2. Find the cube roots of each of the following integers: -125 (ii) -5...

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  3. Show that: (i)27 ^(1/3)X\ 64 ^(1/3)=\ (27X 64) ^(1/3) (ii)(64X\ 72...

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  4. Find the cube root of each of the following numbers: (i)8\ x\ 125 (...

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  5. Evaluate: (i) root(3)(4^3×6^3) (ii) root(3)( 8×17×17×17) (iii) root(...

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  6. Find the cube root of each of the following rational numbers: (-125)...

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  7. Find the cube root of each of the following rational numbers: 0.001...

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  8. Evaluate each of the following : root(3)(27) + root(3)(0.008) + root...

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  9. Show that : (i) (729)^(1/3)/(1000)^(1/3)= (729/1000)^(1/3) (ii) (-51...

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  10. (i) ∛(125×27) = 3 × ...... (ii) ∛(8×…..) = 8 (iii) ∛1728 = 4 × ….. (iv...

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  11. The volume of a cubical box is 474.552 cubic metres. Find the lengt...

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  12. Three numbers are to one another 2 : 3 : 4 . The sum of their cubes is...

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  13. Find the side of a cube whose volume is (24389)/(216)\ m^3dot

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  14. Evaluate: (i) 36^(1/3)X\ 384^(1/3)\ \ \ (ii)96^(1/3) \ X\ 144^(1/3)...

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  15. Find the cube roots of the numbers 2460375, 20346417, 210644875, 570...

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  16. Find the units digits of the cube root of the following numbers: (i)...

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  17. Using cube root tables, find the cube root of (i) 62            (i...

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  18. Find the cube root of 448.

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  19. Find the cube root of 17064.

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  20. Using cube root table, find the value of ((51)/(125000))^(1/3)

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