Question

please answer this full page it's urgent I am giving you full 25 points

Answer 1

question 1 )

√2 and √3 are irrational number

√2 = 1.414 (approx)
√3 = 1.73(approx)

thus 1.5 lies between √2 and √3 which is also rational

question no. 2)

let N = 1.99999. ..... ----1 st

multiply by 10 both side

10N = 19.99999......---2nd

now 2nd - 1st

9N = 18

N = 2

thus answer is 2


question no. 3)

2^(1/3) ,2^(1/4),

32^(1/12)= 2^(5/12)

product

= 2^(1/3)*2^(1/4)*2^(5/12)

= 2^((1/3)+(1/4)+(5/12))

= 2^(12/12)

= 2
thus answer 2

question no.4)

81^(-2/4)

= 81^(-1/2)

= 1/√81

= 1/9

so answer is 1/9


question no 5)

(256)^0.16 *(256)^0.09

= (256)^(0.16+0.09)

= 256^(0.25)

= 2^(8*0.25)

= 2^2 = 4

answer is 4


now last question no. 6))

option a)
x^(12/7)-x^(5/7) ≠ X

so a is wrong

option b)


x^(4/(12*3)

= x^(1/9) ≠x
so option b is incorrect


option c ))

x^((3/2)*(2/3) = X

thus option c is correct

Answer 2

1.A
2.B
3.C
4.D
5.A
6.A
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