Cubes and Cube Roots Test

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Cubes and Cube Roots Test - 17

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Weekly Quiz Competition

Question 1
1 / -0

If $$\displaystyle 27={ a }^{ 3 }$$, find the value of $$a$$.

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

Given, $$a^3=27$$.
Prime factorising, we get,
$$27=3\times 3 \times 3$$.
Also, $$a=\sqrt[3]{a^3}$$.
Then, the value of $$a=\sqrt[3]{27}=\sqrt[3]{3^3}=3$$
$$\implies a=3$$.
Hence, option $$C$$ is correct.
Question 2
1 / -0

If the unit's digit of cube of a number is $$6 $$, then what is the unit's digit of the number itself?

A
$$2$$

B
$$4$$

C
$$6$$

D
$$8$$

Solution

Given, the units digit of cube of a number is $$6$$.

Any number having $$6$$ in it's unit's place will have a $$6$$ in the unit's place of cube.It can be observed $$...6\times ...6\times ...6=......6$$
Therefore if the unit's digit of the cube is $$6$$, the number must have $$6$$ in it's unit's place.
Hence, option $$C$$ is correct.
Question 3
1 / -0

The ______ of a number is a number, whose multiplication by three times gives that number.

A
cube root

B
square root

C
permutation

D
repeating

Solution

The cube root of a number is a number, when multiplication by three times gives that number.

Example: $$2 \times 2 \times 2 = 8.$$
Here, the cube root of a number $$8$$, i.e. $$\sqrt[3]{8}=2$$ is a number, when multiplication by three times ($$2\times2\times2$$) gives that number, i.e.$$8$$.

Therefore, option $$A$$ is correct.
Question 4
1 / -0

What is the unit digit of $$\displaystyle { 100001 }^{ 3 }$$?

A
$$1$$

B
$$0$$

C
$$3$$

D
$$4$$

Solution

Given, the number is $$100001^3$$.
Here, the units digit is $$1$$.
We know, the cube of $$1$$, i.e. $$1^3=1$$, whose units place is $$1$$.
Therefore, the units digit of the cube of $$100001$$, i.e. $$100001^3$$ is $$1$$.
Hence, option $$A$$ is correct.
Question 5
1 / -0

If a number is multiplied three times, then the number is called _____ of the final number.

A
square root

B
cube root

C
absolute value

D
negative

Solution

If a number is multiplied three times, then the number multiplied is called cube root of the number.

Example: Consider the number $$2$$.
Then, $$2 \times 2 \times 2 = 8$$.
Thus, the number $$2$$ is multiplied $$3$$ times to give cube of the number $$2$$.

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

$$1728$$ is an example of _____ of a number $$12$$.

A
square

B
cube

C
Ramanujan number

D
none of these

Solution

Prime factorising $$1728$$, we get,
$$1728$$ $$=(2\times2\times2)\times(2\times2\times2)\times(3\times3\times3)\\=2^3\times 2^3\times 3^3\\=12^3.$$

$$\therefore$$ $$5832$$ is the cube of number $$12$$.

Hence, option $$B$$ is correct.
Question 7
1 / -0

Which odd number needs to be taken out to form a cube number?
$$5 + 7 + 9 + 11$$

A
$$7$$

B
$$5$$

C
$$9$$

D
$$11$$

Solution

We know,
$$\displaystyle 1=1={ 1 }^{ 3 }$$,
$$\displaystyle 3+5=8={ 2 }^{ 3 }$$,
$$\displaystyle 7+9+11=27={ 3 }^{ 3 }$$.
Therefore, $$5$$ must be taken out to form a cube number, $$3^3=27$$.
Hence, option $$B$$ is correct.
Question 8
1 / -0

How will you represent $$49$$ as a cube root?

A
$$\sqrt[7]{49}$$

B
$$\sqrt[2]{49}$$

C
$$\sqrt[4]{49}$$

D
$$\sqrt[3]{49}$$

Solution

We know, the cube root is represented by the symbol $$\sqrt[3]{}.$$
Then, the cube root of $$49$$ is written as $$\sqrt[3]{49}.$$

Hence, option $$D$$ is correct.
Question 9
1 / -0

To cube a number, how many times you need to multiply the number with itself?

A
$$1$$ time

B
$$2$$ times

C
$$3$$ times

D
$$4$$ times

Solution

Consider a number $$a$$ has $$b$$ as its cube.
Then, $$b=a\times a\times a$$
So, we need to multiply a number $$3$$ times for it to be a cube.

Hence, option $$C$$ is correct.
Question 10
1 / -0

The cube root of a number is a number when ______ three times gives that number.

A
divided

B
added

C
subtracted

D
multiplied

Solution

The cube root of a number is a number when multiplied three times gives that number.
Example: $$4 \times 4 \times 4 = 64.$$
Here, $$4$$ is the cube root of $$64.$$

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Cubes and Cube Roots Test - 17

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Cubes and Cube Roots Test - 17

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Question 1

$$1$$

$$2$$

$$3$$

$$4$$

Solution

Question 2

$$2$$

$$4$$

$$6$$

$$8$$

Solution

Question 3

cube root

square root

permutation

repeating

Solution

Question 4

$$1$$

$$0$$

$$3$$

$$4$$

Solution

Question 5

square root

cube root

absolute value

negative

Solution

Question 6

square

cube

Ramanujan number

none of these

Solution

Question 7

$$7$$

$$5$$

$$9$$

$$11$$

Solution

Question 8

$$\sqrt[7]{49}$$

$$\sqrt[2]{49}$$

$$\sqrt[4]{49}$$

$$\sqrt[3]{49}$$

Solution

Question 9

$$1$$ time

$$2$$ times

$$3$$ times

$$4$$ times

Solution

Question 10

divided

added

subtracted

multiplied

Solution

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