The Square Root Exercise 1.1.4 belongs to the unit Square Root
Square Root Exercise 1.1.4

Round off the following numbers to 3 decimal places.
 1.5678 ≈ 1.568
 2.84671 ≈ 2.847
 14.56789 ≈ 14.568
 12.987564 ≈ 12.988
 3.3333567 ≈ 3.333

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

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

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.
 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 m^{2}. If additional land, measuring equal area to added to the garden, its area will be
(900+900)^{2} = 1800 m^{2}
Side of the new garden is 1800 m.
A = side x side = (side)^{2} = 42.43m