Understanding Engineering Mathematics

(i) 2^223 (ii) 3^4 /3^2 (iii) 6^3 × 32 /4

(iv) 6^22 −^232 (v) 2^2 × 4 × 25 (vi) 5^6 /10^4

(vii) 3^4223 −^1 (viii) 49× 7 / 212

B.Simplify (write as simplest products of powers of primes)

(i) 3^43632 (ii) 2^342 / 25 (iii)

6223349

2233

(iv) ( 4 × 6 )^6 /( 32 × 42 ) (v) 27^5 / 95 (vi) (− 4 )^3 /(− 12 )^4

(vii)

3246

3 −^32 −^1

(viii)

81 /^327

3223

C.Show that the following are all the same number

2

√

7

3

√

5

,

√

28

√

45

,

14

3

√

35

,

2

√

35

15

,

2

3

√

7

5

,

2

√

7

√

45

,

√

28

3

√

5

,

√

28

45

D.Express in terms of simplest surds

(i)

√

18 (ii)

√

20 (iii)

√

32 (iv)

√

52

(v)

√

512 (vi)

√

396 (vii)

√

108 (viii)

√

63

E.Rationalize

(i)

1

√

7

(ii) −

1

√

3

(iii)

1

√

2 − 1

(iv)

1

4 −

√

10

(v)

√

5 + 1

√

5 − 1

(vi)

√

2 − 2

√

3

√

2 +

√

3

(vii)

√

1

2

+

√

1

4

+

√

1

8

(viii)

√

512 +

√

128 +

√

32

1.3.8 Decimal notation

➤➤

422

➤

A.Express in decimal form, to four decimal places in each case

(i) −^12 (ii)^72 (iii)^23 (iv) −^29

(v)^06 (vi)^18

B. Express as fractions

(i) 0.25 (ii) 0.125 (iii) 72.45 (iv) −0.312

(v) 0.17