Class 8 RD Sharma Solution - Chapter 4 Cubes and Cube Roots - Exercise 4.5

Making use of the cube root table, find the cube root of the following (correct to three decimal places) :

Question 1.  7

Solution: 

We know that 7 lies between 1-100 so using cube root table we will get ∛7 = 1.913

Question 2.  70

Solution: 

We know that 70 lies between 1-100 so using cube root table we will get ∛70 = 4.121

Question 3.  700

Solution: 

We can write 700 as 70×10

Now we can write ∛700 as ∛70 x ∛10 and we will get ∛700 = 8.879

Question 4.  7000

Solution:

We can write 7000 as 70×100

Now we can write ∛7000 as ∛7 × ∛1000

Using cube root table and we get ∛7 = 1.913 and ∛1000 = 10

= 1.913 × 10 = 19.13

Question 5.  1100

Solution: 

We can write 1100 as 11 x 100

Now we can write ∛1100 as ∛11 × ∛100

Using cube root table we get ∛11 = 2.224 and ∛100 = 4.6642

= 2.224 × 4.642 = 10.323

Question 6.  780

Solution: 

We can write 780 as 78×10

We can write ∛780 as ∛78 and ∛10 

Using cube root table we get ∛78 = 4.272 and ∛10 = 2.154

= 4.272 x 2.154 = 9.205

Question 7.  7800

Solution: 

We can write 7800 as 78×100

Now we can write ∛7800 as ∛78 × ∛100

Using cube root table we get ∛78 = 4.273 and ∛100 = 4.6642

= 4.273 × 4.642 = 19.835

Question 8. 1346

Solution: 

Let's find the factors of 1346 and we can write it as 2×673

Now we can write ∛1346 as ∛2 × ∛673

Since 673 lies between 670 & 680 so ∛670 < ∛673 < ∛680

Now using cube root table we get

∛670 = ∛67 x ∛10 = 8.750

∛680 = ∛68 x ∛10 = 8.794

Difference between 680 & 670 is 10.

So the difference in their cube roots are : 8.794 – 8.750 = 0.044

Difference between 673 & 670  is 3.

So the difference in their cube will : (0.044/10) × 3 = 0.0132

∛673 = 8.750 + 0.013 = 8.763

We can write ∛1346 as ∛2 × ∛673

= 1.260 × 8.763 = 11.041

Question 9.  250

Solution:

We can write 250 as 25×100 and further ∛25 x ∛10 

We get 6.3

Question 10.  5112

Solution: 

Let's find the factor of 5112,

We get ∛(2×2×2×3×3×71)

= 2 × ∛9 × ∛71

Using cube root table we get ∛9 = 2.080 & ∛71 = 4.141

= 2 × 2.080 × 4.141 = 17.227

Question 11.  9800

Solution: 

We can write ∛9800 as ∛98 × ∛100

Using cube root table we get ∛98 = 4.610 & ∛100 = 4.642

= 4.610 × 4.642 = 21.40

Question 12.  732

Solution: 

As we know that the value of ∛732 will lie between ∛730 & ∛740

Using cube root table we get ∛730 = 9.004 & ∛740 = 9.045

Now we will use unitary method,

Difference between 740 & 730: (740 - 730) = 10 

So the difference between their cube roots will be : 9.045 – 9.004 = 0.041

Difference between the values: 732 – 730 = 2

Now we will calculate difference in cube root values: (0.041/10) ×2 = 0.008

∛732 = 9.004+0.008 = 9.012

Question 13.  7342

Solution: 

As we know that the value of ∛7342 will lie between ∛7300 & ∛7400

Using cube root table we will get ∛7300 = 19.39 & ∛7400 = 19.48

Now we will use unitary method,

Difference between 7400 & 7300 = 100

So the difference between their cube roots will be : 19.48 – 19.39 = 0.09

Difference between the values : 7342 – 7300 = 42

Now we will calculate difference in cube root values : (0.09/100) × 42 = 0.037

∛7342 = 19.39+0.037 = 19.427

Question 14.  133100

Solution: 

We can write ∛133100 as ∛ 1331 × ∛ 100,

= 11 × ∛100

Using cube root table we get ∛100 = 4.462

= 11 × 4.462 = 51.062

Question 15. 37800

Solution: 

Let us find the factors for 37800

We get ∛(2×2×2×3×3×3×175)

= 2 x 3 x ∛(175)

= 6 × ∛175

As we know that the value of ∛175 will lie between ∛170 & ∛180

Using cube root table we get ∛170 = 5.540 & ∛180 = 5.646

Now we will use Unitary method,

Difference between 180 & 170 = 10

So the difference between their cube roots will be : 5.646 – 5.540 = 0.106

Difference between the values 175 & 170 = 5

So the difference in their cube roots will be = (0.106/10) × 5 = 0.053

∛175 = 5.540 + 0.053 = 5.593

∛37800 = 6 × ∛175 = 6 × 5.593 = 33.558

Question 16.  0.27

Solution: 

We can write ∛0.27 as ∛27/∛100

By using cube root table we get ∛27 = 3 & ∛100 = 4.642

∛0.27 = ∛27/∛100

= 3/4.642 = 0.646

Question 17.  8.6

Solution: 

∛8.6 = ∛86/∛10

By using cube root table we get ∛86 = 4.414 & ∛10 = 2.154

∛8.6 = ∛86/∛10

= 4.414/2.154 = 2.049 

Question 18.  0.86

Solution:

∛0.86 = ∛86/∛100

By using cube root table we get ∛86 = 4.414 & ∛100 = 4.642

∛8.6 = ∛86/∛100

= 4.414/4.642 = 0.9508

Question 19.  8.65

Solution: 

∛8.65 = ∛865/∛100

As we know that value of ∛865 will lie between ∛860 & ∛870

Using cube root table we get ∛860 = 9.510 & ∛870 = 9.546 & ∛100 = 4.642

We will use Unitary method,

Difference between the values 870 & 860 = 10

So, the difference in their cube roots will be : 9.546 – 9.510 = 0.036

Difference between the values 865 - 860 = 5

So, the difference between their cube roots will be : (0.036/10) × 5 = 0.018

∛865 = 9.510 + 0.018 = 9.528

∛8.65 = ∛865/∛100

= 9.528/4.642 = 2.0525

Question 20.  7532

Solution: 

As we know that value of ∛7532 will lie between ∛7500 & ∛7600

Using cube root table we get ∛7500 = 19.57 & ∛7600 = 19.66

Now we will use Unitary method,

Difference between the values 7600 & 7500 : 7600 - 7500 = 100

So the difference between their cube roots will :19.66 – 19.57 = 0.09

Difference between the values 7532 – 7500 = 32

So the difference between their cube root will : (0.09/100) × 32 = 0.029

∛7532 = 19.57 + 0.029 = 19.599

Question 21.  833

Solution: 

As we know that value of ∛833 will lie between ∛830 and ∛840

Using cube root table we get ∛830 = 9.398 & ∛840 = 9.435

We will use Unitary method,

Difference between the values 840 & 830 = 840 – 830 = 10

So, the difference in their cube root values will be : 9.435 – 9.398 = 0.037

Difference between the values 833 & 830 = 3

So, the difference in their cube root values will be = (0.037/10) ×3 = 0.011

∛833 = 9.398+0.011 = 9.409

Question 22.  34.2

Solution: 

∛34.2 = ∛342/∛10

As we know that value of ∛342 will lie between ∛340 & ∛350

Using cube root table we get ∛340 = 6.980 & ∛350 = 7.047 & ∛10 = 2.154

We will use Unitary method,

Difference between the values 350 & 340 = 10

So, the difference in cube root values will be : 7.047 – 6.980 = 0.067

Difference between the values 342 & 340 = 2

So, the difference in their cube root values will be = (0.067/10) × 2 = 0.013

∛342 = 6.980 + 0.013 = 6.993

∛34.2 = ∛342/∛10

= 6.993/2.154 = 3.246

Question 23.  What is the length of the side of a cube whose volume is 275 cm³. Make use of the table for the cube root.

Solution: 

Given that,

Volume of the cube = 275cm3

Let us assume that the side of the cube as ‘a’ cm

As we know that Volume of Cube : a^3 = 275

a = ∛275

Now we know that the value of ∛275 will lie between ∛270 & ∛280

Using cube root table we get ∛270 = 6.463 & ∛280 = 6.542

We will use Unitary method,

Difference between the values 280 & 270 = 10

So the difference in their cube root will = 6.542 – 6.463 = 0.079

Difference between the values 275 & 270 = 5

So the difference in their cube roots will be = (0.079/10) × 5 = 0.0395

∛275 = 6.463 + 0.0395 = 6.5025