Belongs to the unit 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

 

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

(i) 12

Solution:

√(12) = 3.4641 ≈ 3.464

 

(ii) 18

Solution:

√(1.8) = 1.3416 ≈ 1.341

 

(iii) 133

Solution:

√(133) = 11.5325 ≈ 11.533

 

(iv) 12.34

Solution:

√(12.34) = 3.5128 ≈ 3.513

 

(v) 8.6666

Solution:

√(8.6666) = 2.9439 ≈ 2.944

 

(vi) 234.234

Solution:

√(234.234) = 15.3047 ≈ 15.305

 

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

(i) 13

Solution:

√(13) = 3.60555 ≈ 3.605

 

(ii) 8.12

Solution:

√(8.12) = 2.84956 ≈ 2.8496

 

(iii) 3333

Solution:

√(3333) = 57.73214 ≈ 57.7321

 

 

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

(i) 5

Solution:

√(5) = 2.236067

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

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

 

(ii) 8

Solution:

√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.

 

5. 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.

A = side x side = (side)² = 42.43m