Finding Cube Roots Using Prime Factorization

Q. Which of the following number is both perfect square and perfect cube?

1. 64
2. 36
3. 216
4. 343

Q. Find the cube root of 658503 without prime factorization method.

1. 78
2. 87
3. 67
4. 72

Q. What is the smallest number by which 8192 must be divided so that quotient is a perfect cube?
Also, find the cube root of the quotient so obtained.

Q.

Which is the smallest number that must be multiplied to 77175 to make it a perfect cube?

1. 35

2. 15

3. 30

4. 21

Q.

Is $128$ a perfect cube.

Find its cube root.

Q.

What is the least number by which 10125 should be divided so that the quotient is a perfect cube?

1. 4

2. 5

3. 2

4. 3

Q. Question 1(ix)
Find the cube root of each of the following numbers by prime factorization method:
175616

Q.

Question 1(ii)
Find the cube root of each of the following numbers by prime factorization method:
512

Q.

Question 1(iii)
Find the cube root of each of the following numbers by prime factorization method:
10648

Q. Question 1(v)
Find the cube root of each of the following numbers by prime factorization method:
15625

Q. Which of the following number is both perfect square and perfect cube?

1. 64
2. 36
3. 216
4. 343

Q. What is the easiest and the fastest method to find cube roots ?

Q.

With what least number must 8640 be divided so that the quotient is a perfect cube?

1. 5

2. 6

3. 10

4. 15

Q.

What should be multiplied to 43200 to make it a perfect cube?

1. 2

2. 3

3. 5

4. $\frac{1}{25}$

Q.

224 can be factorized as:

1. $2^5\times 7$
2. $2^4\times$ 7
3. $2^5\times 7^2$
4. $3^2\times 7$

Q.

Find the smallest number by which 1715 be divided so that the quotient is a perfect cube

1. 1

2. 7

3. 5

4. Already a perfect cube

Q.

Find the value of $\sqrt[3]{3343}$ + $\sqrt[3]{3\frac{512}{125}}$

1. 8.5

2. 8.6

3. 8$\frac{4}{5}$

4. 8$\frac{3}{5}$

Q.

Which of these is not a perfect cube?

1. 343

2. 81

3. 1331

4. 512

Q.

Find the value of $\sqrt[3]{35}\times \sqrt[3]{350}\times \sqrt[3]{3500}$.

1. 500

2. 125

3. 50

4. 25

Q. $36\times 24$ written as a product of its primes is

1. $2\times 2\times 2\times 2\times 2\times 3\times 3\times 3$
2. $2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3$
3. $2\times 2\times 2\times 3\times 3$
4. $2\times 2\times 2\times 2\times 2\times 3\times 3$

Q.

Find the smallest number by which 8768 must be divided so that the quotient is a perfect cube.

1. 137

2. 64

3. 128

4. 274

Q. Which of the following number is both perfect square and perfect cube?

1. 343
2. 36
3. 216
4. 64

Q. For the non- perfect cube $243$, find the smallest number by which it must be
$\left(ii\right)$Divided so that the quotient is a perfect cube

Q. Multiply 137592 by the smallest number so that the product is a perfect cube. Also, find the cube root of the product. [4 MARKS]