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}