Applications of Square Roots in Everyday Life

Q.

A rectangle courtyard 3.78 metres long and 5.25 metres wide is to be paved exactly with square tiles, all of the same size what is the largest size of the tile which could be used for the ppurpose ?

Q.

Find the least number which must be subtracted from 18265 to make it a perfect square.

1. 56

2. 40

3. 30

4. 45

Q.

Find the least number which must be added to 306452 to make it a perfect square.

1. 345

2. 465

3. 464

4. 324

Q. How to find the square root of any 3 digit number

Q.

Students are standing in a school assembly line in such a way that the number of rows is equal to the number of columns. If the total number of students is 36, then, how many rows and columns will be there?

1. 3

2. 6

3. 12

4. 18

Q.

The area of a square plot is 1225 $m^2$. What is the length of its side?

1. 55 m

2. 35 m

3. 45 m

4. 25 m

Q.

Find the least four-digits number that is a perfect square.

1. 1300

2. 1024

3. 1765

4. 1200

Q.

In a class, some chocolates were distributed to the students. The number of chocolates given to each student is exactly the same as the number of students in the class. If a total of 676 chocolates were distributed among the students, how many students are there in the class?

1. 22

2. 28

3. 26

4. 24

Q. There are 1000 students in a school. They have to stand in such a way that the number of rows are equal to the number of columns. How many students would be left out in this arrangement?

1. 24
2. 39
3. 64
4. 100

Q.

The area of a square plot is $784{\text{m}}^2$. The side of the square is

1. 38 m

2. 32 m

3. 28 m

4. 21 m

Q. Find the smallest multiple of 112 which is a perfect square.

1. 784

Q. What must be added to 14360 so that the number becomes a perfect square?

1. 40

Q.

If the area of a square plot is $676{\text{m}}^2$, then the side of the square plot is _____

1. 28 m

2. 26 m

3. 24 m

4. 34

Q. In a hall, 576 chairs are arranged in rows and columns with the number of rows equal to the number of columns. The chairs from one row and one column are removed. How many chairs are removed?

1. 49
2. 47
3. 57
4. 59

Q.

In a hall, 225 chairs are arranged in such a way that the number of rows is equal to the number of columns. If one more row and column of chairs is added, find the new number of chairs in the hall.

1. 246

2. 256

3. 265

4. 276

Q.

A square plot has an area of 961 $m^2$. The length of the rope (in m) which extends between two poles located on two adjacent corners of the square is 31m.

1. true

2. false

Q.

Square root of 400 is 20.

1. false

2. true

Q. Find the least number that must be added to 1729 to get a perfect square.

1. 48
2. 30
3. 42
4. 35

Q.

In a hall, 324 chairs are arranged in such a way that the number of rows is equal to the number of columns. If one extra row and one extra column of chairs is added, find the new number of the chairs.

1. 324

2. 381

3. 361

4. 376

Q.

In a hall, 576 chairs are arranged in row and column with the number of rows equal to the number of columns. The chairs in one row and one column is removed. How many chairs are removed?

1. $49$

2. $47$

3. $57$

4. $59$

Q.

What is the least number that should be added to 6200 to make it a perfect square?

1. 41

2. 79

3. 34

4. 80

Q.

Given a square of side 10 m and a rectangle of length 11m and breadth 9 m. Which one has more area?

1. Square

2. Both have the same area

3. Cannot be determined

4. Rectangle

Q. If the area of a square is equal to the area of a rectangle with length and breadth respectively 54 m and 24 m, then the length of the square is m.

1. 26
2. 34
3. 36
4. 46

Q.

Which number must be subtracted from 1786 to make it a perfect square?

1. 22

2. 26

3. 20

4. 24

Q. A square is drawn by joining the mid points of the sides of a square. A third square is drawn inside the second square in the same way and the process is continued infinitely. If the side of the square is $10$ cm, then the sum of areas of all the squares so formed is

1. $100$ cm${}^2$
2. $200$ cm${}^2$
3. $250$ cm${}^2$
4. None of these

Q.

A rectangle whose length and breadth is 32m and 8m respectively has to be converted to a square with the same area. What will be the side of the square?

1. 16.93

2. 15.98

3. None of these

4. 17.97

Q. The ratio of radius is $5:6$ Find ratio of areas

Q.

In a class, there are 529 students who are arranged in rows and columns to form a square for a P.T display. Now the teacher wants to add one more row and column for which 60 more students volunteer. Find the number of students who will not be part of the P.T display.

1. 17

2. 13

3. 19

4. 20

Q.

A teacher wants to arrange 2800 students in a field such that the number of rows is equal to the number of columns. Find the number of rows if 96 were left out after the arrangement.

1. 52

2. 56

3. 54

4. 58

Q.

What must be subtracted from 1729 to get a perfect square?

1. 58

2. 68

3. 48

4. 78