Cubes and Cube Roots Test

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Cubes and Cube Roots Test - 13

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Weekly Quiz Competition

Question 1
1 / -0

Find the smallest number by which the following number must be divided to obtain a perfect cube.
135

A
5

B
6

C
7

D
8

Solution

$$Factorization\quad of\quad 135$$

$$135\quad =\quad 3\times3\times3\times5$$

$$=\quad 3^{ 3 }\times5$$

$$To\quad make\quad a\quad perfect\quad cube,\quad we\quad need\quad to\quad have\quad multiples\quad of\quad 3\quad a\quad powers\quad of\quad prime\quad factors,\\ i.e,\quad we\quad divide\quad the\quad number\quad by\quad 5$$
Question 2
1 / -0

Find the smallest number by which the following number must be divided to obtain a perfect cube.
81

A
3

B
6

C
7

D
14

Solution

Writing 81 as a product of prime factors, we have
$$81=\underline {3\times 3\times 3}\times 3$$
Clearly, to make it a perfect cube, it must be divided by 3.
Question 3
1 / -0

Cube of $$(-2)$$ is _______.

A
$$+8$$

B
$$-8$$

C
$$-4$$

D
$$+4$$

Solution

Cube of $$(-2)$$ is:
$$(-2)^3=(-2)\times (-2)\times (-2)$$
$$=-8$$.

Hence, option $$B$$ is correct.
Question 4
1 / -0

The number $$x$$ which when multiplied by itself three times gives a cube number $$y$$. Then, $$x$$ is a _____ of $$y$$.

A
cube root

B
square root

C
cube

D
none of these

Solution

Given, $$y=x\times x\times x$$.
Then, $$\sqrt[3] y =x$$.
Thus, $$x$$ is a cube root of $$y$$.

Hence, option $$A$$ is correct.
Question 5
1 / -0

An odd cube number will have a/an ___ cube root.

A
odd

B
even

C
fraction

D
none of these

Solution

We know, a cube of an even number ($$\text{applicable to any multiple of an even number}$$) will always be even.
Then, cube root of an odd number can never be even.
This rules out option $$B$$.

We also know, there are perfect cubes which are odd numbers ($${27, 125, 343}$$, etc.)
Therefore, not all odd cube number need to be a fraction.
This rules out option $$C$$.

We know, when $$2$$ or more odd numbers are multiplied, the resulting number will always be odd.
Then, any cube of an odd number will also given an odd number.
Therefore, any odd perfect cube will always have a $$\text{odd} $$ cube root.

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

An even cube number will have _____ cube root.

A
an even

B
an odd

C
a fractional

D
None of the above

Solution

We know, even numbers end with: $$0,2,4,6,8$$.
Also, cubes of these even numbers will end with: $$0,8,64,216,512$$.
$$\therefore$$ They end in $$0,8,4,6,2$$ respectively, which makes the cubes of an even number, an even number.
Thus even cube will have an even cube root.

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

Cube of $$\displaystyle \left ( \frac{1}{5} \right )$$ is

A
-125

B
$$\displaystyle -\frac{1}{125} $$

C
$$\displaystyle -\frac{1}{5} $$

D
$$\displaystyle +\frac{1}{125} $$

Solution

$$\displaystyle \frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}=\frac{1}{125}$$
Question 8
1 / -0

Find the value of: $$\displaystyle \sqrt[3]{3375}$$.

A
$$25$$

B
$$35$$

C
$$15$$

D
None of these

Solution

On prime factorising, we get,
$$3375=\underline{3\times 3\times 3}\times \underline{5\times 5\times 5}$$
$$=3^3\times 5^3$$.
Then, value of $$\sqrt[3]{3375}$$ is:
$$\sqrt[3]{3375}=\sqrt[3]{3^3 \times 5^3}= 3\times5=15$$.
Therefore, option $$C$$ is correct.
Question 9
1 / -0

Find the value of: $$\displaystyle \sqrt[3]{8000}$$.

A
$$10$$

B
$$40$$

C
$$20$$

D
None of these

Solution

On prime factorising, we get,
$$8000=\underline{2\times 2\times 2}\times \underline{2\times 2\times 2}\times \underline{5\times 5\times 5}$$
$$=2^3\times 2^3\times 5^3$$.
Then, value of $$\sqrt[3]{8000}$$ is:
$$\sqrt[3]{8000}=\sqrt[3]{2^3 \times 2^3 \times 5^3}= 2\times2\times5=20$$.
Therefore, option $$C$$ is correct.
Question 10
1 / -0

Finding cube root is the inverse operation of finding the _____ .

A
cube

B
square

C
reciprocal

D
none of these

Solution

Let $$y=x\times x\times x$$.
So, $$\sqrt[3] y =x$$.

Thus, $$x$$ is a cube root of $$y$$
and $$y$$ is the cube of $$x$$.

Thus, we can say that finding cube root is the inverse of finding cube.

Hence, option $$A$$ is correct.

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Re-Attempt Weekly Quiz Competition

Cubes and Cube Roots Test - 13

Result

Cubes and Cube Roots Test - 13

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SHARING IS CARING

Question 1

5

6

7

8

Solution

Question 2

3

6

7

14

Solution

Question 3

$$+8$$

$$-8$$

$$-4$$

$$+4$$

Solution

Question 4

cube root

square root

cube

none of these

Solution

Question 5

odd

even

fraction

none of these

Solution

Question 6

an even

an odd

a fractional

None of the above

Solution

Question 7

-125

$$\displaystyle -\frac{1}{125} $$

$$\displaystyle -\frac{1}{5} $$

$$\displaystyle +\frac{1}{125} $$

Solution

Question 8

$$25$$

$$35$$

$$15$$

None of these

Solution

Question 9

$$10$$

$$40$$

$$20$$

None of these

Solution

Question 10

cube

square

reciprocal

none of these

Solution

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