Cube Root Using Prime Factorisation

Q.

Question 119

Solve the following question:

Three numbers are in the ratio 1 : 2 : 3 and the sum of their cubes is 4500. Find the numbers.

Q. The cube root of $2744$ is

1. $12$
2. $16$
3. $18$
4. $14$

Q.

Find the smallest number by which 26244 should be divided so that the quotient is a perfect cube.

Q. A cube has a volume of 216cm3. The length of the side of the cube (in cm) is

1. $5$
2. $8$
3. $6$
4. $7$

Q.

If x + (1/x) = 6, find x² + (1/x²) and x⁴ +

Q.

The smallest number by which 16384 must be divided so that quotient is a perfect cube is:

1. 4

2. 12

3. None of these

4. 2

Q.

Question 99

Solve the following question:

Is 9720 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube.

Q.

Find the smallest number by which $8788$ must be divided so that the quotient is a perfect cube.

Q.

Question 135

Evaluate: $\sqrt[3]{327}+\sqrt[3]{30.008}+\sqrt[3]{30.064}$

Q.

Question 3(iii)
You are told that 1, 331 is a perfect cube. Can you guess with factorization what is its cube root? Similarly guess the cube roots of
32768

Q.

Find the cube root of $6859$ by prime factorization method.

Q. Three numbers are in the ratio 1 : 2 : 3. The sum of their cubes is 98784. Find the numbers.

1. 14, 20 and 50
2. 14, 28 and 42
3. 17, 42 and 28
4. 14, 28 and 25

Q.

The volume of a cubical box is 474.552 cubic meters. Find the length of each side of the box.

1. 7.8 m
2. 9.2 m
3. 8.3 m
4. 6.9 m

Q. is 46656 a perfect cube?

Q.

Three numbers are to one another 2 : 3 : 4. The sum of their cubes is 0.334125. Find the numbers.

Q.

The value of $\sqrt[3]{3\sqrt{0.000064}}$

1. 0.2

2. 0.0002

3. 0.002

4. 0.02

Q. If volume of the cube is 343 $m^3$ then find the side of the cube

Q.

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

Q.

Question 134

Solve the following question:

Three numbers are in the ratio 2 : 3 : 4. The sum of their cubes is 0.334125. Find the numbers.

Q.

If x + y = 7 and xy = 12, find x² + y².

Q. Find the cube root of 216000.

1. 10
2. 90
3. 60
4. 216

Q. $\text{Simplify:}\sqrt[3]{35-\frac{10}{27}}$

1. $\frac{3}{5}$
2. $\frac{3}{7}$
3. $\frac{5}{3}$
4. $\frac{5}{7}$

Q.

Find the square root of :

(i) 64 (ii) 343 (iii) 729

(iv) 1728 (v) 9261 (vi) 4096

(vii) 8000 (viii) 3375

Q. Value of $\sqrt[3]{3392}\times \sqrt[3]{3448}$ is ______.

1. 50
2. 52
3. 54
4. 56

Q.

Find the smallest number by which the following number must be divided to obtain a perfect cube: $128$

Q.

The volume of a cube is $9261000m^3,$ find the side of the cube.

Q. Three numbers are in the ratio 1:2:3. The sum of their cubes is 7776. Find the numbers.

Q.

Question 61

State whether the following statement is true or false:

Ratio of area of a circle to the area of a square whose side equals radius of circle, is $1:\pi$

Q.

Find the smallest number by which the following number must be divided to obtain a perfect cube: $704$

Q. If 343, 000 is a perfect cube, which of the following is its cube root?

1. 70
2. 170
3. 700
4. 343