squares and square roots work sheet 8th cbse

Word numericals on squares and square roots

1. A SQUARE BoARD HAS 144 sq units.what is the length of each side of board

2.2025 plants are ther in garden such that each row contains as many plants as the number of rows.findd the number of rows and plants in each row

3.what is the length of side of sqare whose area is 441 m2

4.a gardener has 1000 plants.he want to plants in such a way that number of rows and number of columns are same.find the minimum number of plants he wants for this

5.there are 500 children in school.rows should be equal to columns .how many children will be left in doing so

6.a general wishing to arrange his men who are 335250in number in the form of squares found that 9 men were left out.how many men are there in each row

7.major arranges his men in the form of square .in doing so 60 soldiers wer left out.
If total number of soldiers are 8160.find number of soldier sin first row

8.a gardener plants trees in rows and founds that each row has twice number of trees as number of rows.if number of tress are 5408..find number of trees in a h row

9.area of square is 101. 1 /400 it is nixed fraction find the length of each side of plot

10.find number of plants in each row if 1024 plants are kept in such a way that number of rows are equal to number of columns

11. 8649 students are sitting in lecture hall in such a way that number of rows are equal to number of students in each row.
Find total rows

12.a general has 36562 soldiers arranged in such a way that numbe r of rows are equal to number if soldiers in each row .after doing so some soldiers were found to left out .how many are left out

13.the area of play ground is 256.6404 sq mts.fins the length of one side if play ground

14.students of class contributed money each child gave as same as the number if students
Total amount collected was 5184 rs.find the strength of the class

15.Find the length of each side of a square whose area is equal to the area of a rectangle of length 13.6 metres and breadth 3.4 metres.

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

17.The students of a class arranged a picnic. Each student contributed as many rupees as the number of students in the class. If the total contribution is Rs 1156, find the strength of the class.

• 18.In a right triangle ABC, ∠B = 90°. a. If AB = 6 cm, BC = 8 cm, find AC b. If AC = 13 cm, BC = 5 cm, find AB.

18.. Which of the following triplets are Pythagorean?
(i) (8, 15, 17)
(ii) (18, 80, 82)
(iii) (14, 48, 51)
(iv) (10, 24, 26)
(v) (16, 63, 65)
(vi) (12, 35, 38)

19.The product of two numbers is 1296. If one number is 16 times the other, find the numbers.

20.A welfare association collected Rs 202500 as donation from the residents. If each paid as many rupees as there were residents, find the number of residents

21.. A society collected Rs 92.16. Each member collected as many paise as there were members. How many members were there and how much did each contribute?

22.A society collected Rs 2304 as fees from its students. If each student paid as many paise as there were students in the school, how many students were there in the school?

23.The area of a square field is 5184 m2. A rectangular field, whose length is twice its breadth has its perimeter equal to the perimeter of the square field. Find the area of the rectangular field.

24.A PT teacher wants to arrange maximum possible number of 6000 students in a field such that the number of rows is equal to the number of columns. Find the number of rows if 71 were left out after arrangement.

25.The cost of levelling and turning a square lawn at Rs 2.50 per m2 is Rs13322.50 Find the cost of fencing it at Rs 5 per metre.

26.Find the value of:

(i) √80/√405

(ii) √441/√625

(iii) √1587/√1728

(iv) √72 ×√338

(v) √45 × √20


26.The area of a square field is 80 244/729 square metres. Find the length of each side of the field.

27.The area of a square field is 30 1/4m2. Calculate the length of the side of the square.

28.Find the length of a side of a square playground whose area is equal to the area of a rectangular field of dimensions 72m and 338 m.

29.Simplify:

(i) (√59.29 – √5.29)/ (√59.29 + √5.29)

(ii) (√0.2304 + √0.1764)/ (√0.2304 – √0.1764)



30.Evaluate √50625 and hence find the value of √506.25 + √5.0625

31.Find the value of √103.0225 and hence find the value of
(i) √10302.25
(ii) √1.030225

32.   Find the square root of 144 by the method of repeated subtraction.

33. Find the smallest number by which 1800 must be multiplied so that it becomes a perfect square. Also find the square root of the perfect square so obtained.

34. Is 2352 a perfect square? if not, find the smallest number by which 2352 must be multiplied so that the product is a perfect square. Find the square root of new number.

35. The area of a square field is 8281 m2. Find the length of its side.

36  Find the square root of 


37  Simplify:

              


38.Factorise: p2 – 10p + 25.

39.1225 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.

40.Find the smallest number by which 3645 should be divided so as to get a perfect square. Also, find the square root of the number so obtained.

41.For each of the following numbers, find the smallest number by which we divide it so as to get a perfect square. Also find the square root of the square numbers so obtained.

        (a) 37845

(b) 2800

(c) 45056

42.The students of Class VIII of a school donated Rs 2401 for Prime Minister��s National Relief Fund. Each student donated as many rupees as the number of students in the Class. Find the number of students in the Class.

43. There are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement?

44.A school collected Rs 2304 as fees from its students. If each student paid as many paise as there were students in the school, how many students were there in the school?

45.2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.

46.10404 students are sitting in a lecture room in such a manner that there are as many students in a row as there are rows in a lecture room. How many students are there in each row of a lecture room?