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### Math Assignment Class VIII | Cube & Cube Root CH-2

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# **MATH
ASSIGNMENT CLASS VIII | CUBE
& CUBE ROOT**

*Download or Print, free assignment with answer key for Class 8 Cube & Cube Root. Important and extra questions that cover all topics of Cube & Cube Root and is useful and helpful for the students.*

## Math Assignment Class VIII | Cube & Cube Root

**Question 1**

Find the smallest number by which 2250 must be multiplied so that the product is perfect cube.

Answer: 12

Find the smallest number by which 2250 must be multiplied so that the product is perfect cube.

Answer: 12

**Question 2**

Find the value of x if

Find the value of x if

**Answer: - 0.0008**

**Question 3**

Find cube root of 175616 and use it to find the value of

Find cube root of 175616 and use it to find the value of

**Answer: 6.16**

**Question 4**

Find the value of

Find the value of

**Answer: 80/7**

**Question 5**

Find the smallest number by which 8192 must be divided so that the quotient is a perfect cube.

Find the smallest number by which 8192 must be divided so that the quotient is a perfect cube.

**Answer: 4**

**Question 6**

Three numbers are in the ratio 3 : 4 : 5 and the sum of their cubes is 1728. Find numbers.

Three numbers are in the ratio 3 : 4 : 5 and the sum of their cubes is 1728. Find numbers.

**Answer: 6, 8, 10**

**Solution Hint:**

**Let numbers are 3x, 4x, 5x**

**ATQ (3x)**

^{3}+ (4x)^{3}+ (5x)^{3}= 1728**27x ^{3} + 64x^{3} + 125x^{3} = 1728**

**216x ^{3} = 1728**

**x ^{3} = 1728 / 216 = 8**

**x = 2**

**Required numbers are**

**3x = 3 x 2 = 6**

**4x = 4 x 2 = 8**

**5x = 5 x 2 = 10**

**Question 7**

Evaluate:

Evaluate:

**Answer: 3.24**

**Question 8**

Write the cubes of all natural numbers between 1 and 20 and verify the following statements

a) Cubes of all odd natural numbers are odd.

b) Cubes of all even natural numbers are even.

Write the cubes of all natural numbers between 1 and 20 and verify the following statements

a) Cubes of all odd natural numbers are odd.

b) Cubes of all even natural numbers are even.

**Question 9**

Write cubes of 5 natural numbers which are multiples of 3 and verify the cube of natural number, which is multiple of 3 is multiple of 27.

Write cubes of 5 natural numbers which are multiples of 3 and verify the cube of natural number, which is multiple of 3 is multiple of 27.

**Solution Hint**

**Let first 5 multiples of 5 are: 3, 6, 9, 12, 15**

**3**

^{3}**= 27 = 27 x 1**

**6**

^{3}**= 216 = 27 x 8**

**9**

^{3}**= 729 = 27 x 27**

**12**

^{3}**= 1728 = 27 x 64**

**15**

^{3}**= 3375 = 27 x 125**

**In all these cases we see that the cube of 3, 6, 9, 12, 15 is also the multiple of 27**

**Hence prove the required result.**

**Question 10**

Which of the following are perfect cube

i)1728 ii) 106480.

Which of the following are perfect cube

i)1728 ii) 106480.

**Answer: (i) 1728 is a perfect cube**

**(ii) 106480 is not a perfect cube**

**Question 11**

Which is the smallest number by which 392 must be multiplied so that the product is a perfect cube?

Which is the smallest number by which 392 must be multiplied so that the product is a perfect cube?

**Answer: 7**

**Question 12**

What is the smallest number by which 8640 must be divided so that the quotient is a perfect cube?

What is the smallest number by which 8640 must be divided so that the quotient is a perfect cube?

**Answer: 5**

**Question 13**

If one side of a cube is 13 metres, find its volume.

If one side of a cube is 13 metres, find its volume.

**Answer: 13 x 13 x 13 = 2197**

**Question 14**

Find the cube roots i) 343 ii) 1000

Find the cube roots i) 343 ii) 1000

**iii) 2744 iv) 74088**

**Answer: (i) 7 (ii) 10 (iii) 14 (iii) 42**

**Question 15**

Multiply 137592 by the smallest number so the product is a perfect cube and also find the cube root of product.

Multiply 137592 by the smallest number so the product is a perfect cube and also find the cube root of product.

**Answer**

**Prime factors of 137592 = 2 x 2 x 2 x 3 x 3 x 3 x 7 x 7 x 13**

**So if we multiply this number by 7 x 13 x 13 = 1183 then it becomes a perfect cube**

**137592 x 1183 =**

**162771336 is a perfect cube**

**Question 16**

The volume of a cube is 343 cubic metres, find one side of cube.

The volume of a cube is 343 cubic metres, find one side of cube.

**Answer: 7m**

**Question 17**

Divide the number 26244 by the smallest number so that quotient is a perfect cube. Also find the cube root of the quotient

Divide the number 26244 by the smallest number so that quotient is a perfect cube. Also find the cube root of the quotient

**Solution Hint:**

**Prime factors of 26244 = 2 x 2 x 3 x 3 x**

__3 x 3 x__

__3__x__3 x__

__3 x 3__**If we divide this number by**

**2 x 2 x 3 x 3 = 36, then it becomes a perfect cube**

**26244 ÷ 36 = 729**

**Question 18**

The volume of cube 512 cubic metre. Find the length of the side of the cube.

The volume of cube 512 cubic metre. Find the length of the side of the cube.

**Answer: 8m**

**Question 19**

Find the cube roots of each of the following numbers

Find the cube roots of each of the following numbers

**i) 8 X 64 ii) - 216 X 1728 iii) 27 X (- 2744)**

**iv) -125 X -3 375 v) - 456533 vi) - 5832000**

**Answer: (i) 8 (ii) -72 (iii) - 3 x 14 = 42 (iv) 75 (v) -77 (vi) -180**

**Question 20**

Three numbers are in the ratio 1 : 2 : 3. The sum of their cubes is 972. Find the numbers.

Three numbers are in the ratio 1 : 2 : 3. The sum of their cubes is 972. Find the numbers.

**Answer**

**Solution Hint**

**Let numbers are: x, 2x, 3x**

**(x) ^{3} + (2x)^{3} + (3x)^{3} = 972**

** x ^{3} + 8x^{3} + 27x^{3} = 972**

** 36 x ^{3} = 972**

** x ^{3} = 972 / 36**

** x ^{3} = 27 ⇒ **

**x = 3**

**Question 21**

Difference in two perfect cubes is 189. If the cube root of smaller number is 3. Find the cube roots of the larger number.

Difference in two perfect cubes is 189. If the cube root of smaller number is 3. Find the cube roots of the larger number.

**Answer: Larger number = 6**

**Solution Hint**

**Let two numbers are a and b**

**a ^{3} – b^{3} = 189 and b
= 3**

**a ^{3} – (3)^{3} = 189**

**a ^{3} – 27 = 189**

**a ^{3} = 189 + 27**

**a ^{3} = 216 ⇒ **

**a = 6**

**Question 22**

Evaluate:

Evaluate:

**Answer: 8**

**Question 23**

Evaluate:

Evaluate:

**Answer: 3/16**

**THANKS FOR YOUR VISIT**

**PLEASE COMMENT BELOW**

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