Everything Maths Grade 11

CHAPTER 4. ERROR MARGINS 4.2

Example 1: Simplification and Accuracy

QUESTION

Calculate^3

√

54 +^3

√

16. Write the answer to three decimal places.

SOLUTION

Step 1 : Simplify the expression

√ (^3) 54 +√ (^3) 16 = √ (^327) .2 +√ (^38). 2
=^3

√

27.^3

√

2 +^3

√

8.^3

√

2

= 3

√ 3

2 + 2

√ 3

2

= 5^3

√

2

Step 2 : Convert any irrationalnumbers to decimal numbers

5

√ 3

2 = 6, 299605249...

Step 3 : Write the final answerto the required numberof decimal places.

6 , 299605249... = 6, 300 (to three decimal places)

∴^3

√

54 +^3

√

16 = 6, 300 (to three decimal places).

Example 2: Simplification and Accuracy 2

QUESTION

Calculate

√

x + 1+^13

�

(2x + 2)− (x + 1) if x = 3, 6. Write the answer to twodecimal places.

SOLUTION

Step 1 : Simplify the expression