Cubes and Cube Roots Test

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Cubes and Cube Roots Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

$$(35)^3=$$?

A
$$42875$$

B
$$44875$$

C
$$43005$$

D
None of these

Solution

$$\displaystyle 35=7\times 5$$
$$\displaystyle \therefore \quad { \left( 35 \right) }^{ 3 }={ \left( 7 \right) }^{ 3 }\times { \left( 5 \right) }^{ 3 }$$
$$\displaystyle =7\times 7\times 7\times 5\times 5\times 5$$
$$\displaystyle =343\times 125$$
$$\displaystyle =42875$$
$$\displaystyle \therefore $$ The cube of $$35 = 42875.$$
Question 2
1 / -0

Find the unit digit of the cube root of the following number: $$13824$$

A
$$8$$

B
$$6$$

C
$$4$$

D
$$2$$

Solution

The unit's digit of $$13824$$ is $$4.$$
The only numbers whose cubes end with $$4$$ are the numbers which have $$4$$ in their unit's place. Hence cube root of $$13824$$ has $$ 4$$ in unit's place.
Question 3
1 / -0

For an integer $$a,$$ choose the correct statement.

A
$$\displaystyle { a }^{ 3 }$$ is always greater than $$\displaystyle { a }^{ 2 }$$.

B
$$\displaystyle { a }^{ 3 }$$ is always smaller than $$\displaystyle { a }^{ 2 }$$.

C
$$\displaystyle { a }^{ 2 }$$ is always greater than $$\displaystyle { a }^{ 3 }$$.

D
None of the above

Solution

False, since the square of 1 is 1 is equal to the cube of 1. In this case $$\displaystyle { a }^{ 3 }$$ is not greater than $$a^2$$.
Question 4
1 / -0

Find the unit digit of the cube root of the following number:
$$175616$$

A
$$5$$

B
$$6$$

C
$$8$$

D
$$9$$

Solution

And the unit digit of cube root of $$6$$ is $$6$$

$$\therefore$$The unit digit of the cube root of $$175616$$ is $$6.$$
Question 5
1 / -0

Find the unit digit of the cube root of the following number: $$226981$$

A
$$3$$

B
$$5$$

C
$$7$$

D
$$1$$

Solution

The unit's digit of $$226981$$ is $$1.$$
Since $$\displaystyle { \left( 1 \right) }^{ 3 }=1$$, the unit's digit of the cube root of $$226981$$ is $$1.$$
Question 6
1 / -0

Find the unit digit of the cube root of the following number: $$571787$$

A
$$5$$

B
$$4$$

C
$$3$$

D
$$7$$

Solution

The unit's digit of $$571787$$ is $$7.$$
Since $$\displaystyle { \left( 3 \right) }^{ 3 }=27$$, the unit's digit of the cube root of $$571787$$ is $$3.$$
Question 7
1 / -0

What is the last digit (one's place) of $$\displaystyle { 143 }^{ 3 }?$$

A
$$3$$

B
$$9$$

C
$$7$$

D
$$1$$

Solution

Given, the number is $$143^3$$.
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 $$143$$, i.e. $$143^3$$ is $$7$$.
Hence, option $$C$$ is correct.
Question 8
1 / -0

What will be the unit digit of $$\displaystyle { 98765 }^{ 3 }$$.

A
$$5$$

B
$$0$$

C
$$2$$

D
$$3$$

Solution

Given, the number is $$98765^3$$.
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 $$98765$$, i.e. $$98765^3$$ is $$5$$.
Hence, option $$A$$ is correct.
Question 9
1 / -0

Find the digit at unit's place of $$\displaystyle { 128 }^{ 3 }$$.

A
$$8$$

B
$$6$$

C
$$4$$

D
$$2$$

Solution

Given, the number is $$128^3$$.
Here, the units digit is $$8$$.
We know, the cube of $$8$$, i.e. $$8^3=512$$, whose units place is $$2$$.
Therefore, the units digit of the cube of $$128$$, i.e. $$128^3$$ is $$2$$.
Hence, option $$D$$ is correct.
Question 10
1 / -0

Cube of $$0.9$$ is:

A
$$0.0729$$

B
$$7.29$$

C
$$729$$

D
$$0.729$$

Solution

Cube of $$0.9$$:
$$\displaystyle { 0.9 }^{ 3 }=0.9\times 0.9\times 0.9$$
$$\displaystyle =0.729$$.

Hence, option $$D$$ is correct.

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Re-Attempt Weekly Quiz Competition

Cubes and Cube Roots Test - 16

Result

Cubes and Cube Roots Test - 16

Score

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Rank

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SHARING IS CARING

Question 1

$$42875$$

$$44875$$

$$43005$$

None of these

Solution

Question 2

$$8$$

$$6$$

$$4$$

$$2$$

Solution

Question 3

$$\displaystyle { a }^{ 3 }$$ is always greater than $$\displaystyle { a }^{ 2 }$$.

$$\displaystyle { a }^{ 3 }$$ is always smaller than $$\displaystyle { a }^{ 2 }$$.

$$\displaystyle { a }^{ 2 }$$ is always greater than $$\displaystyle { a }^{ 3 }$$.

None of the above

Solution

Question 4

$$5$$

$$6$$

$$8$$

$$9$$

Solution

Question 5

$$3$$

$$5$$

$$7$$

$$1$$

Solution

Question 6

$$5$$

$$4$$

$$3$$

$$7$$

Solution

Question 7

$$3$$

$$9$$

$$7$$

$$1$$

Solution

Question 8

$$5$$

$$0$$

$$2$$

$$3$$

Solution

Question 9

$$8$$

$$6$$

$$4$$

$$2$$

Solution

Question 10

$$0.0729$$

$$7.29$$

$$729$$

$$0.729$$

Solution

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