## SURDS – EXERCISE 1.3.3 β Class 9

1. Write the following surds in their simplest form:

(i) βππ

= β(19 Γ 4)

= β(19 Γ24)

= πβππ

(ii) β (πππ)

= β(33 Γ 22)

= β22

= βπ

(iii) βππππ

= β5000

= β(511 Γ 84)

= πβπ

(iv) βπππ/ππ

= β[(33 Γ 7)/52]

= 3βπ/ππ

(v) βπππ/ππ

= β(24 Γ 52)/724

= 2β52/72

= 2βππ/ππ

1. Classify the following in to like surds

(i) βππ , βπππ , βππ , βππ , βππ , βππ

= β35 , β27 , β(52Γ3) , β(32Γ23) , β(2 Γ 33) , β(23Γ3)

= 32β3 , 23β2 , 5β3 , 3×2β2 , 3β(2×3), 2β(2×3)

= 9β3, 8β2, 5β3, 6β2, 3β6, 2β6

= {8β2, 6β2}, {9β3, 5β3}, {2β6, 3β6,}

={ βπππ, βππ}, { βπππ, βππ}, { βππ, βππ,}

(ii) βππππ, βπππ, βπππ, βπππ, βπππ, βππ

= β(2Γ52), β(73Γ2), β(63Γ 3), β(53Γ3), β(43Γ2), β(23Γ 3)

= 10β2, 7β2, 6β3, 5β3, 4β2, 2β3

= {4βπ, 7βπ, 10βπ} & {2βπ, 5βπ, 6βπ}

= { βππππ, βπππ , βπππ} & { βπππ, βπππ, βππ}

1. Which of the following are pure surds?

(i) β296 = β(33Γ37) = 2β(37Γ2) = 2βππ β not pure surds

(ii) β729 = β36 = 33 = 27 βΒ  not pure surds

(iii) β 211 Cannot be reduced further hence it is a pure surd. β Yes, a pure surd

(iv) β 75 is also a pure surd. β Yes, a pure surds

(v) β 296 Β = β(23Γ37) = 2 βππ β no, not a pure surd

(vi) β296 = cannot be reduced further, hence it is a pure surd β Yes

1. Write the following irrational numbers sure from

(i) β(ππβ(ππ))

= β27 = β33 = 3β3

= [15(27)1/2]1/2

= 152/4 x 271/4 Β Β Β Β Β Β Β Β Β Β Β Β [1/2 = 4/2]

= β(153 Γ 27)

= β(225 Γ 27)

= βππππ

Β

(ii) β(ππ(βππ))

= [40 Γ (12)1/2] Β½

= (40)1/2 Γ (12)1/4

= β(402 Γ (12)1)

= β(402Γ 121)

= β(1600Γ12)

= β19200

(iii) β(π(βππ))

= [51/2 Γ(48)1/2]Β½

= [51/2 Γ 481/4]

= β (52Γ 48)

= β(25Γ48)

= β1200

5. Reduce the following to surds of the same order.

(i) β , βπand π1/5

The orders are 3, 2, and 5

LCM of 2, 3 and 5 is 30

β2 = 21/3 = 210/30 = (πππ) 1/3π

β2 = 21/2 = 215/30 = (πππ ) 1/3π

51/5 = 51/5 = 56/30 = (ππ) 1/3π

(1024)1/3π , (32768) 1/3π , (15625) 1/3π

They have the same order 30

(ii) βπ , (βππ)1/4 , and (βππ)1/8

Order is 2, 4, 8

Their LCM is 8

β5 = 51/2 = 54/8 = (54 )1/8 = (125)1/8

(β15)1/4 = (β15)1/4 = (15)2/8 = ((15)2) 1/8 = (225)1/8

(50)1/8 is in its simplest form

(50)1/8 Β , ππππ , ππππ

β΄ Thus they all are of the same order 8.

(iii) βπ , βπ1/3 , (βππ)1/4 and (βππππ)π/1π

Order is 2, 3, 4, and 12

Their LCM is 12

β2 = 21/2 = 26/12 = (β26)1/12 = (64)1/12

β71/3 = 74/12 = (74 )1/12 = (2401)1/12

(β11)1/4 = (11)3/12 = ((11)3)1/12 = (1331)1/12

167112 is in its simplest form

πππ/1π , πππππ/1π , πππππ/1π , πππππ/1π

β΄ Thus they all are of the same order 12

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