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Cubes and Cube Roots Test - 15

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Cubes and Cube Roots Test - 15
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  • Question 1
    1 / -0
    Write the units digit of the cube of $$833$$.
    Solution

    Given, the number is $$833$$.

    Here, the units digit is $$3$$.

    We know, the cube of $$3$$, i.e. $$3^3=27$$, whose units place is $$7$$.

    Therefore, the units digit of the cube of $$833$$ is $$7$$.

    Hence, option $$B$$ is correct.

  • Question 2
    1 / -0
    No perfect cube can end with exactly: 
    Solution
    A perfect cube of a number is obtained by multiplying the number by itself three times.
    Eg: $${ 1 }^{ 3 } = 1\times1\times1= 1$$
    $$ { 2 }^{ 3 } =2\times2\times2 =8$$
    $$ { 3 }^{ 3 }=3\times3\times3 = 27  $$.
    Similarly, $${ 10 }^{ 3 } = 10 \times 10 \times 10 = 1000$$.

    So, perfect cubes can never end with one or two zeroes and have to end with exactly $$3$$ zeroes or number of zeros equal to the multiple of $$3$$.

    Hence, option $$A$$ is correct.
  • Question 3
    1 / -0
    From the following options, choose the option with which perfect cube does not ends with:
    Solution
    We know, 
    $$1^3 = 1$$
    $$2^3 = 8$$
    $$3^3 = 27$$
    $$4^3 = 64$$
    $$5^3 = 125$$
    $$6^3 = 216$$
    $$7^3 = 343$$
    $$8^3 = 512$$
    $$9^3 = 729$$
    $$10^3 = 1000$$.

    A number ending with $$1, 2, 3, 4, 5, 6, 7, 8, 9, 0$$ has 
    perfect cubes ending with $$1, 8, 7, 4, 5, 6, 3, 2, 9, 0$$, respectively.
    Hence, option $$D$$ is correct.
  • Question 4
    1 / -0
    Write the units digit of the cube for $$125125125$$.
    Solution

    Given, the number is $$125125125$$.

    Here, the units digit is $$5$$.

    We know, the cube of $$5$$, i.e. $$5^3=125$$, whose units place is $$5$$.

    Therefore, the units digit of the cube of $$125125125$$ is $$5$$.

    Hence, option $$A$$ is correct.

  • Question 5
    1 / -0
    Write the units digit for the cube of $$5922$$.
    Solution

    Given, the number is $$5922$$.

    Here, the units digit is $$2$$.

    We know that, for the cube of $$2$$, i.e. $$2^3=8$$, the unit digit is $$8$$.

    Therefore, the units digit of the cube of $$5922$$ is $$8$$.

    Hence, option $$A$$ is correct.

  • Question 6
    1 / -0
    $$(56)^3=$$?
    Solution
    $$\displaystyle 56=7\times 8$$
    $$\displaystyle \therefore \quad { \left( 56 \right)  }^{ 3 }={ \left( 7 \right)  }^{ 3 }\times { \left( 8 \right)  }^{ 3 }$$
    $$\displaystyle =7\times 7\times 7\times 8\times 8\times 8$$
    $$\displaystyle =343\times 512$$
    $$\displaystyle =175616$$
    $$\displaystyle \therefore $$ The cube of $$56 = 175616.$$
  • Question 7
    1 / -0
    $$(402)^3=$$?
    Solution
    $$\displaystyle 402=2\times 3\times 67$$
    $$\displaystyle \therefore \quad { \left( 402 \right)  }^{ 3 }={ \left( 2 \right)  }^{ 3 }\times { \left( 3 \right)  }^{ 3 }\times { \left( 67 \right)  }^{ 3 }$$
    $$\displaystyle =2\times 2\times 2\times 3\times 3\times 3\times 67\times 67\times 67$$
    $$\displaystyle =8\times 27\times 300763$$
    $$\displaystyle =64964808$$
    $$\displaystyle \therefore $$ The cube of $$402 = 64964808.$$
  • Question 8
    1 / -0
    $$(72)^3=$$?
    Solution
    $$\displaystyle 72=8\times 9$$
    $$\displaystyle \therefore \quad { \left( 72 \right)  }^{ 3 }={ \left( 8 \right)  }^{ 3 }\times { \left( 9 \right)  }^{ 3 }$$
    $$\displaystyle =8\times 8\times 8\times 9\times 9\times 9$$
    $$\displaystyle =512\times 729$$
    $$\displaystyle =373248$$
    $$\displaystyle \therefore $$ The cube of $$72 = 373248.$$
  • Question 9
    1 / -0
    Write the units digit of the cube for $$44447$$.
    Solution

    Given, the number is $$44447$$.

    Here, the units digit is $$7$$.

    We know, the cube of $$7$$, i.e. $$7^3=343$$, whose units place is $$3$$.

    Therefore, the units digit of the cube of $$44447$$ is $$3$$.

    Hence, option $$A$$ is correct.

  • Question 10
    1 / -0
    Cube root of $$343$$.
    Solution

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