## RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.3

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.3

**Other Exercises**

- RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.1
- RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.2
- RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.3
- RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.4
- RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.5

**Question 1.**

**Find the cube roots of the following numbers by successive subtraction of numbers : 1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397,**

**(i) 64**

**(ii) 512**

**(iii) 1728**

**Solution:**

**(i) 64**

64 – 1 = 63

63 – 7 = 56

56 – 19 = 37

37 – 37 = 0

∴ 64 = (4)^{3}

∴ Cube root of 64 = 4

**(ii) 512**

512 -1 =511

511- 7 = 504

504 – 19 = 485

485 – 37 = 448

448 – 61 = 387

387 – 91 =296

296 – 127 = 169

169 – 169 = 0

∴ 512 = (8)^{3}

∴ Cube root of 512 = 8

**(iii) 1728**

1728 – 1= 1727

1727 -7 = 1720

1720 -19 = 1701

1701 -37= 1664

1664 – 61 = 1603

1603 – 91 = 1512

1512 -127= 1385 .

1385 – 169= 1216

1216 – 217 = 999

999 – 271 =728

728 – 331 = 397

397 – 397=0

∴ 1728 = (12)^{3}

∴ Cube root of 1728 = 1^{2}

**Question 2.**

**Using the method of successive subtraction, examine whether or not the following numbers are perfect cubes :**

**(i) 130**

**(ii) 345**

**(iii) 792**

**(iv) 1331**

**Solution:**

**(i) 130**

130 – 1 = 129

129 -7 = 122

122 -19 = 103

103 -37 = 66

66 – 61 = 5

We see that 5 is left

∴ 130 is not a perfect cube.

**(ii) 345**

345 – 1 = 344

344 – 7 = 337

337 – 19 = 318

318 – 37 = 281

81 – 61 =220

220 – 91 = 129

129 – 127 = 2

We see that 2 is left

∴ 345 is not a perfect cube.

**(iii) 792**

792 – 1 = 791

791 – 7 = 784

784 – 19 = 765

765 – 37 = 728

728 – 61 = 667

667 – 91 = 576

576 – 127 = 449

449 – 169 = 280

∴ We see 280 is left as 280 <217

∴ 792 is not a perfect cube.

**(iv) 1331**

1331 – 1 = 1330

1330 -7 = 1323

1323 – 19 = 1304

1304 – 37 = 1267

1267 – 61 = 1206

1206 – 91 = 1115

1115 – 127 = 988

988 – 169 = 819

819 – 217 = 602

602 – 271 = 331

331 – 331 =0

∴ 1331 is a perfect cube

**Question 3.**

**Find the smallest number that must be subtracted from those of the numbers in question 2, which are not perfect cubes, to make them perfect cubes. What are the corresponding cube roots ?**

**Solution:**

We have examined in Question 2, the numbers 130, 345 and 792 are not perfect cubes. Therefore

**(i) 130**

130 – 1 = 129

129 -7= 122

122 -19 = 103

103 – 37 = 66

66 – 61 = 5

Here 5 is left

∴ 5 < 91 5 is to be subtracted to get a perfect cube.

Cube root of 130 – 5 = 125 is 5

**(ii) 345**

345 – 1 = 344

344 -7 = 337

337 – 19 = 318

318 – 37 = 281

281 – 61 =220

220 – 91 = 129

129 – 127 = 2

Here 2 is left ∵ 2 < 169

∴ Cube root of 345 – 2 = 343 is 7

∴ 2 is to be subtracted to get a perfect cube.

**(iii) 792**

792 – 1 = 791

791 – 7 = 784

784 – 19 = 765

765 – 37 = 728

728 – 61 =667

667 – 91 = 576 5

76 – 127 = 449

449 – 169 = 280

280 – 217 = 63

∴ 63 <217

∴ 63 is to be subtracted

∴ Cube root of 792 – 63 = 729 is 9

**Question 4.**

**Find the cube root of each of the following natural numbers :**

**(i) 343**

**(ii) 2744**

**(iii) 4913**

**(iv) 1728**

**(v) 35937**

**(vi) 17576**

**(vii) 134217728**

**(viii) 48228544**

**(ix) 74088000**

**(x) 157464**

**(xi) 1157625**

**(xii) 33698267**

**Solution:**

**Question 5.**

**Find the smallest number which when multiplied with 3600 will make the product a perfect cube. Further, find the cube root of the product.**

**Solution:**

Grouping the factors in triplets of equal factors, we see that 2, 3 x 3 and 5 x 5 are left

∴ In order to complete the triplets, we have to multiply it by 2, 3 and 5.

∴ The smallest number to be multiplied = 2×2 x 3 x 5 = 60

Now product = 3600 x 60 = 216000 and cube root of 216000

**Question 6.**

**Multiply 210125 by the smallest number so that the product is a perfect cube. Also, find out the cube root of the product.**

**Solution:**

Grouping the factors in triplets of equal factors, we see that 41 x 41 is left

∴ In order to complete the triplet, we have to multiply it by 41

∴ Smallest number to be multiplied = 41

∴ Product = 210125 x 41 = 8615125

∴ Cube root of 8615125

**Question 7.**

**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.**

**Solution:**

Grouping the factors in triplets of equal factors, we see that 2 is left

∴ Dividing by 2, we get the quotient a perfect cube

∴ Perfect cube = 8192 + 2 = 4096

**Question 8.**

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

**Solution:
**Ratio in numbers =1:2:3

Let first number = x

Then second number = 2x

and third number = 3x

∴ Sum of cubes of there numbers = (x)

^{3}+ (2x)

^{3}+(3x)

^{3}

**Question 9.
**

**The volume of a cube is 9261000 m**

^{3}. Find the side of the cube.**Solution:**

Hope given RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.3 are helpful to complete your math homework.

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