Breath Math

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

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.

2. (1.234)²

Solution:

(1.234)² = 1.522756

Hence, there are 6 digits after the decimal points.

3. (0.0023)²

Solution:

(0.0023)² = 0.00000529

Hence, there are 8 digits after the decimal points.

4. (1.001)³

Solution:

(1.001)³ = 1.003003001

Hence, there are 9 digits after the decimal points.

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2. 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.

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© 1.844164

Solution:

The square root of 1.844164 will have 3 digits in it.

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(d) 0.0089510521

Solution:

The square root of 0.0089510521 will have 5 digits in it.

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3. Find the square root of the following numbers using division method;

(1) 651.7809

Solution:

Therefore, √(651.7809) = 25.53

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(2) 0.431649

Solution:

Therefore, √(0.431649) = 0.657

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(3) 95.4529

Solution:

Therefore, √(95.4529) = 9.77

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(4) 73.393489

Solution:

Therefore, √(73.393489) = 8.567

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4. 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 24686.6944m²

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