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# Square root Exercise 1.1.3

Belongs to the unit Square Root

Exercise 1.1.3

1. 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. (1.234)2

Solution:

(1.234)2 = 1.522756

Hence, there are 6 digits after the decimal points.

1. (0.0023)2

Solution:

(0.0023)2 = 0.00000529

Hence, there are 8 digits after the decimal points.

1. (1.001)3

Solution:

(1.001)3 = 1.003003001

Hence, there are 9 digits after the decimal points.

1. 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.

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.

1. 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

1. A square garden has an are 24686.6944m2. 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 24686.6944m2

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 m2