Belongs to the unit 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 24686.6944m2. 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 24686.6944m^{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}