Cubes and Cube Roots Test

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Cubes and Cube Roots Test - 10

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Weekly Quiz Competition

Question 1
1 / -0

Find the cube root of the following number by prime factorisation method:
$$64$$

A
$$2$$

B
$$4$$

C
$$8$$

D
$$10$$

Solution

Prime factorising, we get,
$$64 = 2\times2\times2\times2\times2\times2 $$
$$= \underline {4\times4\times4} $$.

Here, the factor $$4$$ occur as triplet. Hence, it is a perfect cube.

Therefore, cube root of $$64$$, i.e. $$\sqrt[3]{64} = 4$$.
Question 2
1 / -0

Cube of any odd number is even.

A
True

B
False

C
Depends on the number

D
Data Insufficient

Solution

We know, cube of any odd number is odd.
Eg. The cube of the odd number $$3$$ is $$27$$, which is an odd number.

Hence, the given statement is false.
Therefore, option $$B$$ is correct.
Question 3
1 / -0

There is no perfect cube which ends with $$8$$.

A
True

B
False

C
Insufficient Data

D
None of these

Solution

We know, cube of $$2$$, i.e. $$2^3=8$$.
Here, $$8$$ is a perfect cube.
That is, there is at least one perfect cube which ends with $$8$$.
Hence, the given statement is false.
Therefore, option $$B$$ is correct.
Question 4
1 / -0

Find the cube root of the following number by prime factorisation method:
$$512$$

A
$$6$$

B
$$8$$

C
$$7$$

D
$$9$$

Solution

Prime factorising, we get,
$$512 = \underline{2\times2\times2}\times\underline{2\times2\times2}\times\underline{2\times2\times2} $$
$$= \underline {8\times8\times8} $$.
Here, the factor $$8$$ occur as triplet. Hence, it is a perfect cube.

Therefore, cube root of $$512$$, i.e. $$\sqrt[3]{512} = 8$$.
Question 5
1 / -0

$$8640$$ is not a perfect cube.

A
True

B
False

C
Ambiguous

D
Data insufficient

Solution

Prime factorization of:
$$ 8640=2^6 \times 3^3 \times 5^1$$.

We know, a perfect cube has multiples of $$3$$ as powers of prime factors.

Here, $$8640$$ is not a perfect/complete cube.
That is, the given statement is true.

Hence, option $$A$$ is correct.
Question 6
1 / -0

Cubes of negative integers are negative.

A
True

B
False

C
Ambiguous

D
Data insufficient

Solution

Multiplication of three negative numbers (i.e. the cube), will always be negative.
Eg.: $$(-4)^3=-4\times -4 \times -4=16\times -4=-64$$, which is negative.

That is, the given statement is true.
Therefore, option $$A$$ is correct.
Question 7
1 / -0

$$\sqrt[3]{216}$$ is:

A
Less than $$6$$

B
Greater than $$6$$

C
Equal to $$6$$

D
Equal to $$9$$

Solution

Prime factorising, we get,
$$216= 6\times6\times6=6^3$$.

Then,
$$\sqrt[3]{216} = \sqrt[3] {6^3} = 6$$.

Hence, option $$C$$ is correct.
Question 8
1 / -0

Cube of all odd natural numbers are odd.

A
True

B
False

C
Ambiguous

D
Data insufficient

Solution

We know, the multiplication of $$3$$ odd numbers, i.e. the cube of an odd natural number, will always be odd.

For example, consider the odd natural numbers $$3$$ and $$5$$.

Then, their cube is $$3^3=27$$ and $$5^3=125$$, whose units place is odd.

That is, the cubes are also odd.

Hence, we can say, a cube of all odd natural numbers is odd.

Therefore, the given statement is true, and option $$A$$ is correct.
Question 9
1 / -0

Cubes of all even natural numbers are even.

A
True

B
False

C
Ambiguous

D
Data insufficient

Solution

We know, the cube of an even natural number, will always be even

Example: Consider the even natural numbers $$2$$ and $$4$$.
Then, their cubes are $$2^3=8$$ and $$4^3=64$$, which are even numbers

Thus, we can show, cubes of all even natural numbers are even.
Therefore, the given statement is true and option $$A$$ is correct.
Question 10
1 / -0

What is the least number by which $$8640$$ is divided, the quotient as a complete cube number?

A
$$6$$

B
$$7$$

C
$$5$$

D
$$8$$

Solution

$$Prime\quad factorization\quad of\quad 8640,\\ 8640\quad =\quad 2^{ 6 }*3^{ 3 }*5\\ A\quad perfect\quad cube\quad has\quad multiples\quad of\quad 3\quad as\quad powers\quad of\quad prime\quad factors\\ i.e,\quad 8640\quad has\quad to\quad be\quad divided\quad by\quad 5\quad to\quad be\quad a\quad perfect\quad cube$$

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Re-Attempt Weekly Quiz Competition

Cubes and Cube Roots Test - 10

Result

Cubes and Cube Roots Test - 10

Score

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Rank

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SHARING IS CARING

Question 1

$$2$$

$$4$$

$$8$$

$$10$$

Solution

Question 2

True

False

Depends on the number

Data Insufficient

Solution

Question 3

True

False

Insufficient Data

None of these

Solution

Question 4

$$6$$

$$8$$

$$7$$

$$9$$

Solution

Question 5

True

False

Ambiguous

Data insufficient

Solution

Question 6

True

False

Ambiguous

Data insufficient

Solution

Question 7

Less than $$6$$

Greater than $$6$$

Equal to $$6$$

Equal to $$9$$

Solution

Question 8

True

False

Ambiguous

Data insufficient

Solution

Question 9

True

False

Ambiguous

Data insufficient

Solution

Question 10

$$6$$

$$7$$

$$5$$

$$8$$

Solution

User

Question Analysis

My Perfomance

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Rank

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