The Square Root Exercise 1.1.3 belongs to the chapter Square Root.
Square Root Exercise 1.1.3

How many digits are there after the decimal points in the following?
(1) (3.16)^{2}
Solution:
(3.16)^{2} = 9.9856
Hence, there are 4 digits after the decimal points.
 (1.234)^{2}
Solution:
(1.234)^{2} = 1.522756
Hence, there are 6 digits after the decimal points.
 (0.0023)^{2}
Solution:
(0.0023)^{2} = 0.00000529
Hence, there are 8 digits after the decimal points.
 (1.001)^{3}
Solution:
(1.001)^{3} = 1.003003001
Hence, there are 9 digits after the decimal points.

Given that the numbers below are all squares of some decimal numbers, how many digits do you expect in their square roots?
(a)84.8241
Solution:
The square root of 84.8241 will have 2 digits in it.
(b) 0.085849
Solution:
The square root of 0.085849 will have 3 digits in it.
© 1.844164
Solution:
The square root of 1.844164 will have 3 digits in it.
(d) 0.0089510521
Solution:
The square root of 0.0089510521 will have 5 digits in it.

Find the square root of the following numbers using division method;
(1) 651.7809
Solution:
Therefore, √(651.7809) = 25.53
(2) 0.431649
Solution:
Therefore, √(0.431649) = 0.657
(3) 95.4529
Solution:
Therefore, √(95.4529) = 9.77
(4) 73.393489
Solution:
Therefore, √(73.393489) = 8.567
 A square garden has an are 24686.6944 m². A trench of one meter wide has to be dug along the boundary inside the garden. After digging the trench, what will be the area of the out garden?
Solution:
Area of the square garden is 24686.6944m^{2}
Length of a side of the garden is √(24686.6644) = 157.12 m
If a trench of one meter is dug along the boundary inside the garden the length of a side of the garden will be (157.12 – 2) m = 155.12 m
The area of the remaining garden is (155.12) = 24062.2144 m^{2}