The Square Root Exercise 1.1.4 belongs to the unit Square Root

## Square Root Exercise 1.1.4

### Round off the following numbers to 3 decimal places.

- 1.5678 ≈ 1.568
- 2.84671 ≈ 2.847
- 14.56789 ≈ 14.568
- 12.987564 ≈ 12.988
- 3.3333567 ≈ 3.333

### Find the square root of the following numbers correct to 3 decimal places.

(i) 12

**Solution:**

√(12) = 3.4641 ≈ 3.464

**(ii) 18**

**Solution:**

√(1.8) = 1.3416 ≈ 1.341

**(iii) 133**

**Solution:**

√(133) = 11.5325 ≈ 11.533

**(iv) 12.34**

**Solution:**

√(12.34) = 3.5128 ≈ 3.513

**(v) 8.6666**

**Solution:**

√(8.6666) = 2.9439 ≈ 2.944

**(vi) 234.234**

**Solution:**

√(234.234) = 15.3047 ≈ 15.305

### Find the square root of the following numbers correct to 4 decimal places.

**(i) 13**

**Solution:**

√(13) = 3.60555 ≈ 3.605

**(ii) 8.12**

**Solution:**

√(8.12) = 2.84956 ≈ 2.8496

**(iii) 3333**

**Solution:**

√(3333) = 57.73214 ≈ 57.7321

### Find the approximation from below to 4 decimal places to the square root of the following numbers.

**(i) 5**

**Solution:**

√(5) = 2.236067

(2.236067)^{2 }= 4.9996 < 5 < 5.000009 = (2.23607)^{2}

2.236007 is the approximation from below of √5 to 5 decimal places.

(ii) 8

**Solution:**

√8 = 2.828427

(2.82842)^{2 } = 7.999959 < 8 < 8.000016 = (2.828443)^{2}

2.82842 is the approximation from below of √8, correct to 5 decimal places.

**A square garden has area of 900m2. Additional land measuring equal area, surrounding it, has been added to it. If the resulting plot is also in the form of a square, what is its side correct to 3 decimal places?**

**Solution:**

Ares of square garden is 900 m^{2}. If additional land, measuring equal area to added to the garden, its area will be

(900+900)^{2} = 1800 m^{2}

Side of the new garden is 1800 m.

A = side x side = (side)^{2} = 42.43m