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Cubes and Cube Roots

Question paper, Set 3

  • Set 3 of 10
  • 20 questions
  • 50 marks
  • 1 hour 30 minutes

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Work each question on paper first, then open its answer and solution to check your work.

  1. How do we read x3x^3?
    1 mark
    Answer and solution

    x3=x×x×xx^3 = x \times x \times x

    It is read as 'xx power 3' (or) 'xx cubed'.

    Answer: xx power 3 (or) xx cubed

  2. Write r×r×r×t×t×tr \times r \times r \times t \times t \times t in power form.
    2 marks
    Answer and solution

    r×r×r=r3r \times r \times r = r^3

    t×t×t=t3t \times t \times t = t^3

    ∴r×r×r×t×t×t=r3×t3\therefore r \times r \times r \times t \times t \times t = r^3 \times t^3

    Answer: r3×t3r^3 \times t^3

  3. Write the next number in the pattern 8,27,64,125,…8, 27, 64, 125, \ldots
    1 mark
    Answer and solution

    These are 232^3, 333^3, 434^3, 535^3.

    ∴\therefore the next number is 63=2166^3 = 216

    Answer: 216216

  4. Between the cubes of which two consecutive numbers does 200 lie?
    2 marks
    Answer and solution

    From the table: 53=1255^3 = 125 and 63=2166^3 = 216.

    125<200<216125 < 200 < 216

    So 200 lies between 535^3 and 636^3.

    Answer: Between 535^3 and 636^3

  5. Which of these numbers are cubes? Write each cube as the cube of a number: 27, 36, 64, 81, 100, 125.
    3 marks
    Answer and solution

    Check each number with the table of cubes.

    33=273^3 = 27

    43=644^3 = 64

    53=1255^3 = 125

    The other numbers are not in the table of cubes, so they are not cubes.

    Answer: 27=3327 = 3^3, 64=4364 = 4^3, 125=53125 = 5^3

  6. Fill in the boxes: 133=13×13×13=□×13=□13^3 = 13 \times 13 \times 13 = \square \times 13 = \square
    2 marks
    Answer and solution

    13×13=16913 \times 13 = 169

    169×13=2197169 \times 13 = 2197

    ∴133=169×13=2197\therefore 13^3 = 169 \times 13 = 2197

    Answer: 169169 and 21972197

  7. Asha wrote 143=14×3=4214^3 = 14 \times 3 = 42. (i) What mistake did she make? (ii) Find the correct value of 14314^3 by first finding 14×1414 \times 14. (iii) In the same way, find 12312^3.
    5 marks
    Answer and solution

    (i) She multiplied 14 by 3. But 14314^3 means 14 multiplied by itself 3 times.

    (ii) 14×14=19614 \times 14 = 196, 196×14=2744196 \times 14 = 2744

    (iii) 12×12=14412 \times 12 = 144, 144×12=1728144 \times 12 = 1728

    Answer: (ii) 143=274414^3 = 2744 (iii) 123=172812^3 = 1728

  8. The cube of which number is −343-343?
    1 mark
    Answer and solution

    (−7)3=−73=−343(-7)^3 = -7^3 = -343

    So −343-343 is the cube of −7-7.

    Answer: −7-7

  9. Ravi wrote (−6)3=216(-6)^3 = 216. Is he right? Write the correct value.
    2 marks
    Answer and solution

    (−6)3=(−6)×(−6)×(−6)(-6)^3 = (-6) \times (-6) \times (-6)

    =36×(−6)=−216= 36 \times (-6) = -216

    A negative number multiplied 3 times gives a negative answer, so Ravi is wrong.

    Answer: No. (−6)3=−216(-6)^3 = -216

  10. Find (−11)3(-11)^3 by first finding (−11)×(−11)(-11) \times (-11).
    3 marks
    Answer and solution

    (−11)×(−11)=121(-11) \times (-11) = 121

    121×(−11)=−1331121 \times (-11) = -1331

    ∴(−11)3=−1331\therefore (-11)^3 = -1331

    Answer: −1331-1331

  11. Find the sum of the cubes of 3 and 5.
    1 mark
    Answer and solution

    33+53=27+1253^3 + 5^3 = 27 + 125

    =152= 152

    Answer: 152152

  12. Show that 33+43+53=633^3 + 4^3 + 5^3 = 6^3.
    5 marks
    Answer and solution

    LHS 33+43+53=27+64+1253^3 + 4^3 + 5^3 = 27 + 64 + 125

    =216= 216

    RHS =63=36×6=216= 6^3 = 36 \times 6 = 216

    LHS = RHS = 216

    Answer: Both sides are 216216

  13. Find 33+(−2)33^3 + (-2)^3.
    1 mark
    Answer and solution

    33+(−2)3=27+(−8)3^3 + (-2)^3 = 27 + (-8)

    =27−8= 27 - 8

    =19= 19

    Answer: 1919

  14. Find (−4)3+73(-4)^3 + 7^3.
    2 marks
    Answer and solution

    (−4)3+73=−64+343(-4)^3 + 7^3 = -64 + 343

    =279= 279

    Answer: 279279

  15. By how much is 939^3 more than 636^3?
    2 marks
    Answer and solution

    Difference = 93−639^3 - 6^3

    93−63=729−2169^3 - 6^3 = 729 - 216

    =513= 513

    Answer: 513513

  16. Find 103−12310^3 - 12^3.
    3 marks
    Answer and solution

    123=144×12=172812^3 = 144 \times 12 = 1728

    103−123=1000−172810^3 - 12^3 = 1000 - 1728

    =−728= -728

    Answer: −728-728

  17. Kiran wrote: 123−153=(12−15)3=(−3)3=−2712^3 - 15^3 = (12 - 15)^3 = (-3)^3 = -27. (i) Find the correct value of 123−15312^3 - 15^3. (ii) What was Kiran's mistake?
    5 marks
    Answer and solution

    (i) 123=144×12=172812^3 = 144 \times 12 = 1728

    153=225×15=337515^3 = 225 \times 15 = 3375

    123−153=1728−3375=−164712^3 - 15^3 = 1728 - 3375 = -1647

    (ii) Each number must be cubed first and then subtracted. 123−15312^3 - 15^3 is not (12−15)3(12 - 15)^3.

    Answer: (i) −1647-1647 (ii) He subtracted the numbers before cubing them

  18. Simplify −q3−(−q)3-q^3 - (-q)^3.
    1 mark
    Answer and solution

    (−q)3=−q3(-q)^3 = -q^3

    −q3−(−q3)=−q3+q3=0-q^3 - (-q^3) = -q^3 + q^3 = 0

    Answer: 00

  19. Find (−6)3−(−3)3(-6)^3 - (-3)^3.
    3 marks
    Answer and solution

    (−6)3−(−3)3=−216−(−27)(-6)^3 - (-3)^3 = -216 - (-27)

    =−216+27= -216 + 27

    =−189= -189

    Answer: −189-189

  20. Find the values of: (i) 63+(−6)36^3 + (-6)^3 (ii) 63−(−6)36^3 - (-6)^3 (iii) −63−(−6)3-6^3 - (-6)^3 (iv) −63−63-6^3 - 6^3
    5 marks
    Answer and solution

    63=2166^3 = 216 and (−6)3=−216(-6)^3 = -216

    (i) 63+(−6)3=216+(−216)6^3 + (-6)^3 = 216 + (-216), =216−216= 216 - 216, =0= 0

    (ii) 63−(−6)3=216−(−216)6^3 - (-6)^3 = 216 - (-216), =216+216= 216 + 216, =432= 432

    (iii) −63−(−6)3=−216−(−216)-6^3 - (-6)^3 = -216 - (-216), =−216+216= -216 + 216, =0= 0

    (iv) −63−63=−216−216-6^3 - 6^3 = -216 - 216, =−432= -432

    Answer: (i) 00 (ii) 432432 (iii) 00 (iv) −432-432