RD Sharma Class 8 Math 3rd Chapter Squares and Square Roots Exercise 3.5 Solution

Exercise 3.5

  1. Find the square root of each of the following by long division method:

(i) 12544 

(ii) 97344 

(iii) 286225

(iv) 390625

(v) 363609

(vi) 974169

(vii) 120409

(viii) 1471369

(ix) 291600

(x) 9653449

(xi) 1745041

(xii) 4008004

(xiii) 20657025

(xiv) 152547201

(xv) 20421361

(xvi) 62504836

(xvii) 82264900 

(xviii) 3226694416

(xix) 6407522209 

(xx) 3915380329

Solution:

2.Find the least number which must be subtracted from the following numbers to make them a perfect square:

(i) 2361

(ii) 194491

(iii) 26535

(iv) 16160

(v) 4401624

Solution:

  1. Find the least number which must be added  from the following numbers to make them a perfect square:

(i) 5607             

(ii) 4931                  

(iii) 4515600                

(iv) 37460                      

(v) 506900

 Solution.

  1. Find the greatest number of 5 digits which is a perfect square.

Solution:

We know that the greatest number with five digits is 99999.

To make a perfect square number with five digits, first, find the smallest number that should be subtracted from 99999.

To find the smallest number, use the long division method to find the square root of 99999.

i.e., 99999 – 143 = 99856

Therefore, the greatest number with 5 digits is 99856, which is a perfect square number

5. Find the least number of six digits which is a perfect square.

Solution:

The least number with six digits is 100000. To find the least square number with six digits. we must find the smallest number that must be added to 100000 in order to make a perfect square. For that, we have to find the square root of 100000 by the long division method as follows:

6. Find the greatest number of 4 digits which is a perfect square.

Solution:

The greatest number with four digits is 9999.

To find the greatest perfect square with four digits. We must find the smallest number that must be subtracted from 9999 in order to make a perfect square. For that, we have to find the square root of 9999 by the long division method as shown below:

7. A General arranges his soldiers in rows to form a perfect square. He finds that in doing so, 60 soldiers are left out. If the total number of soldiers be 8160, find the number of soldiers in each row.

Solution:

60 soldiers are left out.

So, Remaining soldiers = 8160 – 60 = 8100

The number of soldiers in each row to form a perfect square would be the square root of 8100.

We have to fund the square root of 8100 by the long division method as shown below:

8. The area of a square field is 60025 m2. A man cycles along its boundary at 18 km/hr. In how much time will he return at the starting point?

Solution:

Area of the square field = 60025 m2

The length of the square field would be the square root of 60025.

Using the long division method:

Hence, the length of the square field is 245 m.

The square has four sides, so the number of boundaries of the field is 4.

The distance s covered by the man = 245 m x 4 = 980 m = 0.98 km

If the velocity v is 18 km/hr, the required time t can be calculated using the following formula:

t = s/v

t = 0.98/18 = 0.054 hr = 3 minutes, 16 seconds

So, the man will return to the starting point after 3 minutes and 16 seconds

9. The cost of leveling and turfing a square lawn at Rs. 2.50 per m2 is Rs. 13322.50. Find the cost of fencing it at Rs. 5 per metres.

Solution:

First, we have to find the area of the square lawn, which the total cost divided by the cost of leveling and turfing per square metre:

Area of a square = 13322.5/2.5 = 5329 m2

The length of one side of the square is equal to the square root of the area. We will use the long division method to find it as shown below:

Therefore, the length of one side of the square = 73m

he circumference of the square is 73 × 4 = 292 m

Hence, the cost of fencing the lawn at Rs. 5 per metre = 292 × 5 = Rs. 1460.

10. Find the greatest number of three digits which is a perfect square.

Solution:

The greatest number with three digits is 999.

To find the greatest perfect square with three digits, we must find the smallest number that must be subtracted from 999 in order to get a perfect square. For that, we have to find the square root by the long division method as shown below:

So, 38 must be subtracted from 999 to get a perfect square.

999 – 38 = 961

961 = 312.

Hence, the greatest perfect square with three digits is 961.

11. Find the smallest number which must be added to 2300 so that it becomes a perfect square.

Solution:

To find the square root of 2300, we use the long division method:

2300 is 4 (704 – 700) less than 482..

Hence, 4 must be added to 2300 to get a perfect square.

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  1. bro awesom,e sir thank u for your help.;/#besteducation website. good boyee

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