MCQ Questions for Class 8 Maths Cubes And Cube Roots Quiz 8

State whether the statements are true (T) or false (F):
The cube of

$0.4$ is

$0.064$ .

0%
True
0%
False

Explanation

The cube of

$0.4$ is:

$(0.4)^3=0.4\times0.4\times0.4=0.064$ .

Hence, the given statement is true.

Therefore, option

$A$ is correct.

State whether the statements are true (T) or false (F).
A number having

$7$ at its units digit will have

$3$ at the units place of its cube.

0%
True
0%
False

Explanation

We know,

square of

$7 = 7 \times 7 \times 7 = 343$ ,
square of

$17 = 17 \times 17 \times 17= 4913$ ,
square of

$27 = 27 \times 27 \times 27=19683$ ,
square of

$37 = 37 \times 37 \times 37= 50653$
and so on.

Therefore, we can say that, a number having

$7$ at its ones will have

$3$ at the units place of its cube.

That is, the given statement is true and option

$A$ is correct.

State whether the statements are true (T) or false (F).
Square of a number is positive, so the cube of that number will also be positive.

0%
True
0%
False

Explanation

Let,

$3$ is a positive number.

Then, square of

$3 = (3)^2= 3 \times 3 = 9$ , which is positive
and cube of

$3 = (3)^3= 3 \times 3 \times 3 = 27$ , which is also positive.

Now let,

$-3$ is a negative number.

Then, square of

$-3 = (-3)^2= -3 \times -3 = 9$ , which is positive
and cube of

$-3 = (-3)^3= -3 \times -3 \times -3 = -27$ , which is negative.

Hence, the given statement is not always true.

That is, the given statement is false and option

$B$ is correct.

State whether the statements are true (T) or false (F).

$363$

$\times$

$81$ is a perfect cube.

0%
True
0%
False

Explanation

Prime factorizing the given numbers, we get,

$363=3 \times 11 \times \times 11$

$81= 3 \times 3 \times 3 \times 3$ .

Then,

$363 \times 81$

$= 3 \times 11 \times 11 \times 3 \times 3 \times 3 \times 3$

$= \underline {3 \times 3 \times 3} \times 3 \times 3 \times 11 \times 11$ .

Here,

$3$ and

$11$ does not occur as triplets.
Therefore,

$363 \times 81$ is not a perfect cube.

That is, the given statement is false and option

$B$ is correct.

State whether the statements are true (T) or false (F).
Each prime factor appears

$3$ times in its cube.

0%
True
0%
False

Explanation

We know, each prime factors appears

$3$ times in its cube.

For example, consider the cube of

$6$ .

That is,

$6^3=(2\times3)^3=2^3 \times 3^3$ .

Here, the prime factors of

$6$ are

$2$ and

$3$ .

Also, in the cube of

$6$ , its prime factors

$2$ and

$3$ appears

$3$ times.

Hence, the given statement is true and option

$A$ is correct.

State whether the statements are true (T) or false (F).
Cube roots of

$8$ are

$+2$ and

$-2$ .

0%
True
0%
False

Explanation

Prime factorising

$8$ and

$-8$ ,

${8}$

$={2\times2\times2}$

${(-8)}$

$={-2\times-2\times-2}$ .

Then, their cube roots,

$\sqrt[3]{8}$

$=\sqrt[3]{2\times2\times2}$

$= 2$

And

$\sqrt[3]{(-8)}$

$=\sqrt[3]{-2\times-2\times-2}$

$= -2$ .

Thus,

$-2$ is the cube root of

$-8$ and

$2$ is the cube root of

$8$

Therefore, the given statement is false and option

$B$ is correct.

State whether the statements are true (T) or false (F).
Cube of an odd number is even.

0%
True
0%
False

Explanation

We know, the multiplication of

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

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, cube of an odd natural numbers are odd.

Therefore, the given statement is false and option

$B$ is correct.

State whether the statements are true (T) or false (F).

$999$ is a perfect cube.

0%
True
0%
False

Explanation

Prime factorising

$999$ :

$999 = 3 \times 3\times 3 \times 37 = \underline{3 \times 3\times 3} \times 37$ .

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

Here, number of $3$ 's is $3$ and number of $37$ 's is $1$ .

Therefore,

$999$ is not a perfect cube.

That is, the given statement is false and option

$B$ is correct.

1650553_1792170_ans_6602b81551e142d4a63b2dcd536713a1.png

State whether the statements are true (T) or false (F).
Cube of an even number is even.

0%
True
0%
False

Explanation

We know, the multiplication of

$3$ even numbers, i.e. the cube of an even natural number, will always be even.

Example, consider the even natural numbers

$2$ and

$4$ .

Then, their cube is

$2^3=8$ and

$4^3=64$ , whose units place is even.

That is, the cubes are also even.

Hence, we can say, cube of an even natural numbers is even.

Therefore, the given statement is true and option

$A$ is correct.

State whether the statements are true (T) or false (F).

$\sqrt[3]{8 + 27} = \sqrt[3]{8} + \sqrt[3]{27}$

0%
True
0%
False

Explanation

$\sqrt[3]{8 + 27}$ is not equal to

$\sqrt[3]{8} + \sqrt[3]{27}$

$\sqrt[3]{8} + \sqrt[3]{27} = \sqrt[3]{2 \times 2 \times 2} + \sqrt[3]{3 \times 3 \times 3} = 2 + 3 = 5$

$\sqrt[3]{8 + 27}$ =

$\sqrt[3]{35} \neq 5$

State whether the statements are true (T) or false (F).
Cube of an odd number is odd.

0%
True
0%
False

Explanation

We know, the multiplication of

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

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, cube of an odd natural numbers are odd.

Therefore, the given statement is true and option

$A$ is correct.

Cube of

$(-\dfrac 12)$ is:

0%
$\dfrac {1}{8}$
0%
$\dfrac {1}{16}$
0%
$-\dfrac {1}{8}$
0%
$-\dfrac {1}{16}$

Explanation

We know,

$(a)^3 =a\times a\times a$ .

Similarly, cube of

$\left(-\dfrac {1}{2}\right)^3$ is:

$\left(-\dfrac {1}{2}\right)^3$

$=\left(-\dfrac {1}{2}\right) \times \left(-\dfrac {1}{2}\right)\times \left(-\dfrac {1}{2}\right)$

$=\left(-\dfrac {1}{8}\right)$

Therefore, cube of

$\left(-\dfrac {1}{2}\right)^3$ is

$-\dfrac {1}{8}$ .

Hence, option

$C$ is correct.

What is the sum of six consecutive odd numbers to form

$216$ ?

0%
$31 + 33 + 35 + 17 + 39 + 41$
0%
$31 + 33 + 35 + 19 + 39 + 41$
0%
$31 + 33 + 35 + 27 + 39 + 41$
0%
$31 + 33 + 35 + 37 + 39 + 41$

Explanation

Given number $216$ is the cube of $6$ , i.e. $6^3=216$ .

We know,

$\displaystyle 1=1={ 1 }^{ 3 }$ ,

$\displaystyle 3+5=8={ 2 }^{ 3 }$ ,

$\displaystyle 7+9+11=27={ 3 }^{ 3 }$ ,

$\displaystyle 13+15+17+19=64={ 4 }^{ 3 }$ ,

$\displaystyle 21+23+25+27+29=125={ 5 }^{ 3 }$ ,

$\displaystyle 31+33+35+37+39+41=216={ 6 }^{ 3 }$ .

$\displaystyle \therefore$ The sum of six consecutive odd numbers are to form $216$ is $\displaystyle 31+33+35+37+39+41=216$ .

Hence, option $D$ is correct.

The cube of a number is 8 times the cube of another number. If the sum of the cubes of numbers is 243, then what is the difference of the numbers?

0%
3
0%
4
0%
6
0%
-6

What is the sum of

$4$ consecutive odd numbers to form

$64$ ?

0%
$13 +15 + 27 + 19 = 64$
0%
$13 +15 + 17 + 19 = 64$
0%
$13 +5 + 17 + 19 = 64$
0%
$3 +15 + 17 + 19 = 64$

Explanation

Given number $64$ is the cube of $4$ , i.e. $4^3=64$ .

We know,

$\displaystyle 1=1={ 1 }^{ 3 }$ ,

$\displaystyle 3+5=8={ 2 }^{ 3 }$ ,

$\displaystyle 7+9+11=27={ 3 }^{ 3 }$ ,

$\displaystyle 13+15+17+19=64={ 4 }^{ 3 }$ .

$\displaystyle \therefore$ The sum of four consecutive odd numbers are to form $64$ is $\displaystyle 13+15+17+19=64$ .

Hence, option $B$ is correct.

The product

$864 \times n$ is a perfect cube. What is the smallest possible value of n ?

0%
2
0%
1
0%
4
0%
3

Let cos

$(\alpha +\beta)= \cfrac 4 5$ and let sin

$(\alpha -\beta)= \cfrac 5 {13}$ , where

$0 \le \alpha, \beta \le \cfrac \pi 4$ , then tan

$2\alpha =$

0%
$\cfrac {56}{33}$
0%
$\cfrac {19}{12}$
0%
$\cfrac {20}{7}$
0%
$\cfrac {25}{16}$

If a number x ends with a prime number, then

$\sqrt [ 3 ]{ x }$ cannot end with the digit

0%
6
0%
3
0%
7
0%
8

If cube of a number is done what will be at unit palced

0%
$5$
0%
$7$
0%
From $0$ to $9$ any one
0%
$4$

CBSE Questions for Class 8 Maths Cubes And Cube Roots Quiz 8 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

CBSE Questions for Class 8 Maths Cubes And Cube Roots Quiz 8 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

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