Question

(2) State which of the following are surds. Justify.

(i) 3√51

(ii) 4√16

(iii) 5√81

(iv) √256

(v) 3√64

(vi)√22/7​

Answer 1

Answer:

parts (i), (vi) are surds

Step-by-step explanation:

(i) 3root 51  = 3root (3*17)

Since it cannot be expressed in rational no., it is a surd

(ii) 4 root 16 = 16

Thus, it is not a surd

(iii) 5root 81 = 45

not a surd

(iv) root 256 = 16

not a surd

(v) 3 root 64 = 24

not a surd

(vi) root (2*11)/7

cannot be expressed as rational no. , thus, it is a surd

Answer 2

Answer:

1 , 3 and 6 are surds

Step-by-step explanation

1) ³√51 is a surd

2) ⁴√2×2×2×20 = ⁴√(2)⁴ = 2

hence , ⁴√16 is not a surd

2) ⁴√2×2×2×20 = ⁴√(2)⁴ = 2

hence , ⁴√16 is not a surd

3) ⁵√81 is a surd

4) ²√256 = ²√(16)² = 16

hence , 256 is not a surd

5) ³√4×4×4 = ³√(4)³ = 4

hence , 64 is not a surd

6) √22 is a surd

7

Hope it helps you