Square Root Exercise 1.1.4 – Square root – Class IX

The Square Root Exercise 1.1.4 belongs to the unit Square Root

Square Root Exercise 1.1.4

  1. Round off the following numbers to 3 decimal places.

  1. 1.5678 ≈ 1.568
  2. 2.84671 ≈ 2.847
  3. 14.56789 ≈ 14.568
  4. 12.987564 ≈ 12.988
  5. 3.3333567 ≈ 3.333

  1. Find the square root of the following numbers correct to 3 decimal places.

(i) 12

Solution:

Square Root Exercise 1.1.4

√(12) = 3.4641 ≈ 3.464


(ii) 18

Solution:

Square Root Exercise 1.1.4

√(1.8) = 1.3416 ≈ 1.341


(iii) 133

Solution:

Square Root Exercise 1.1.4

√(133) = 11.5325 ≈ 11.533


(iv) 12.34

Solution:

Square Root Exercise 1.1.4

√(12.34) = 3.5128 ≈ 3.513


(v) 8.6666

Solution:

Square Root Exercise 1.1.4

√(8.6666) = 2.9439 ≈ 2.944


(vi) 234.234

Solution:

Square Root Exercise 1.1.4

√(234.234) = 15.3047 ≈ 15.305


  1. Find the square root of the following numbers correct to 4 decimal places.

(i) 13

Solution:

Square Root Exercise 1.1.4

√(13) = 3.60555 ≈ 3.605


(ii) 8.12

Solution:

Square Root Exercise 1.1.4

√(8.12) = 2.84956 ≈ 2.8496


(iii) 3333

Solution:

Square Root Exercise 1.1.4

√(3333) = 57.73214 ≈ 57.7321


  1. Find the approximation from below to 4 decimal places to the square root of the following numbers.

(i) 5

Solution:

46

√(5) = 2.236067

(2.236067)= 4.9996 < 5 < 5.000009 = (2.23607)2

2.236007 is the approximation from below of  √5 to 5 decimal places.


(ii) 8

Solution:

47

√8 = 2.828427

(2.82842)2  = 7.999959  <  8 <  8.000016  =  (2.828443)2

2.82842 is the approximation from below of  √8, correct to 5 decimal places.


  1. A square garden has area of 900m2. Additional land measuring equal area, surrounding it, has been added to it. If the resulting plot is also in the form of a square, what is its side correct to 3 decimal places?

Solution:

Ares of square garden is 900 m2. If additional land, measuring equal area to added to the garden, its area will be

(900+900)2 = 1800 m2

Side of the new garden is 1800 m.

Square Root Exercise 1.1.4

A = side x side = (side)2 = 42.43m