Cubes and Cube Roots Test

Result

Cubes and Cube Roots Test - 24

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Directions For Questions

Find the cube root of:

...view full instructions

$$-571787$$

A
$$-73$$

B
$$-83$$

C
$$-93$$

D
$$-63$$

Solution

On prime factorising, we get,
$$571787=\underline{83\times 83\times 83}$$ $$=83^3$$.
Then, $$-571787$$ $$=(-83)^3$$.
Therefore, cube root of $${-571787}$$ is:
$$\sqrt[3]{-571787}=\sqrt[3]{(-83)^3}= -83$$.
Therefore, option $$B$$ is correct.
Question 2
1 / -0

Find the cube root of: $$175616$$.

A
$$56$$

B
$$46$$

C
$$66$$

D
$$76$$

Solution

On prime factorising, we get,
$$ 175616= 8\times8\times8\times7\times7\times7$$
$$= 8^3 \times 7^3$$.
Then, cube root of $$175616$$ is:
$$\sqrt[3]{175616}=\sqrt[3]{8^3 \times 7^3}= 8\times 7\times=56$$.
Therefore, option $$A$$ is correct.
Question 3
1 / -0

By estimation method, $$\sqrt[3]{-13824}=$$?

A
$$-24$$

B
$$-28$$

C
$$-26$$

D
$$-34$$

Solution

Given, $$-13824$$.
The unit's digit of $$13824$$ is $$4,$$ so $$4$$ is the unit's digit of the cube root....[Since, $$4^3=64$$].
Now, grouping the three digits from the right, the number left is $$13.$$
We know, $$\displaystyle { 2 }^{ 3 }=8<13<27={ 3 }^{ 3 }$$.
$$\displaystyle \Rightarrow $$ $$2$$ is the ten's digit of the cube root of $$13824.$$
Then, $$24$$ is the cube root of $$13824.$$
$$\displaystyle \therefore $$ $$-24$$ is the cube root of $$-13824.$$

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

Find the cube root of $$592704$$ using prime factorization:

A
$$86$$

B
$$82$$

C
$$84$$

D
$$88$$

Solution

On prime factorizing, we get,
$$592704 = 2\times2\times2\times2\times2\times2\times3\times3\times3\times7\times7\times7$$
$$= 2^3\times2^3\times3^3\times7^3 \\=84^3.$$

Thus, cube root of $$592704$$ is:
$$\sqrt[3]{592704}=\sqrt[3]{84^3 } \\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =84$$.

Therefore, option $$C$$ is correct.
Question 5
1 / -0

Find the cube root of $$250047$$ using prime factorization:

A
$$63$$

B
$$61$$

C
$$67$$

D
$$65$$

Solution

On prime factorising, we get,
$$250047$$ $$=\underline{3\times3\times3}\times\underline{3\times3\times3}\times\underline{7\times 7\times 7}$$
$$= 3^3\times3^3\times7^3=63^3$$.

Then, cube root of $$250047$$ is:
$$\sqrt[3]{250047}=\sqrt[3]{63^3}= 63$$.

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

$$\sqrt[3]{-226981}=$$?

A
$$-51$$

B
$$-61$$

C
$$-67$$

D
$$-57$$

Solution

On prime factorising, we get,
$$226981=\underline{61\times 61\times 61}$$ $$=61^3$$.
Then, $$-226981$$ $$=(-61)^3$$.
Therefore, value of $$\sqrt[3]{-226981}$$ is:
$$\sqrt[3]{-226981}=\sqrt[3]{(-61)^3}= -61$$.
Therefore, option $$B$$ is correct.
Question 7
1 / -0

Find the cube root of $$438976$$ using prime factorization:

A
$$74$$

B
$$72$$

C
$$76$$

D
$$71$$

Solution

On prime factorising, we get,
$$438976$$ $$=\underline{2\times2\times2}\times\underline{2\times2\times2}\times\underline{19\times 19\times 19}$$
$$= 2^3\times2^3\times19^3=76^3$$.

Then, cube root of $$438976$$ is:
$$\sqrt[3]{438976}=\sqrt[3]{76^3}= 76$$.

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

The smallest number by which $$5400$$ must be multiplied so that it becomes a perfect cube is:

A
$$12$$

B
$$10$$

C
$$5$$

D
$$3$$

Solution

Prime factorising $$5400$$, we get,
$$ 5400 = 3 \times 3 \times 3 \times 5 \times 5 \times 2 \times 2 \times 2$$
$$= 2 ^3 \times 3 ^3 \times 5^2$$.
We know, a perfect cube has multiples of $$3$$ as powers of prime factors.
Here, number of $$2$$'s is $$3$$, number of $$3$$'s is $$3$$ and number of $$5$$'s is $$2$$.
So we need to multiply another $$5$$ to the factorization to make $$5400$$ a perfect cube.
Hence, the smallest number by which $$5400$$ must be multiplied to obtain a perfect cube is $$5$$.
Therefore, option $$C$$ is correct.
Question 9
1 / -0

Find the cube root of $$2744$$ by estimation method.

A
$$12$$

B
$$14$$

C
$$24$$

D
$$16$$

Solution

Step $$I$$: Form groups of $$3$$ starting from right most digit of $$2744$$, i.e. $$\underline{2}\underline{744}$$.
Then, the two groups are $$744$$ and $$2.$$
Here, $$744$$ has $$3$$ digit and $$2$$ has only $$1$$.

Step $$II$$: Take $$744$$.
Digit in unit place $$= 4$$.
Therefore, we take one's place of required cube root as $$4$$ ....[Since, $$4^3=64$$].

Step $$III$$: Now, take the other group $$2$$.
We know, $$\displaystyle { 1 }^{ 3 }=1 $$ and $${ 2 }^{ 3 }=8$$.
Here, the smallest number among $$1$$ and $$2$$ is $$ 1$$.
Therefore, we take $$1$$ as ten's place.
$$\displaystyle \therefore \quad \sqrt[3] { 2744 } =14$$.

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

Cube root of the product of two negative numbers is ____.

A
positive

B
negative

C
positive or negative

D
none of these

Solution

The product of two negative integers, i.e. a negative number when multiplied by another negative number gives a positive number.
Then, the cube root of the resultant positive number will be positive.

E.g.: Let the two integers be $$-4$$ and $$-2$$.
Then, their quotient $$(-4)\times(-2)=8$$, which is positive.
Therefore, $$\sqrt[3]{(-4)\times(-2)}=\sqrt[3]{8}=2$$, which is also positive.

Hence, option $$A$$ is correct.

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Cubes and Cube Roots Test - 24

Result

Cubes and Cube Roots Test - 24

Score

-

Rank

-

SHARING IS CARING

Question 1

$$-73$$

$$-83$$

$$-93$$

$$-63$$

Solution

Question 2

$$56$$

$$46$$

$$66$$

$$76$$

Solution

Question 3

$$-24$$

$$-28$$

$$-26$$

$$-34$$

Solution

Question 4

$$86$$

$$82$$

$$84$$

$$88$$

Solution

Question 5

$$63$$

$$61$$

$$67$$

$$65$$

Solution

Question 6

$$-51$$

$$-61$$

$$-67$$

$$-57$$

Solution

Question 7

$$74$$

$$72$$

$$76$$

$$71$$

Solution

Question 8

$$12$$

$$10$$

$$5$$

$$3$$

Solution

Question 9

$$12$$

$$14$$

$$24$$

$$16$$

Solution

Question 10

positive

negative

positive or negative

none of these

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.