Question

Plz give me answer of 14 and 16 question Question in the picture below. It's urgent

Answer 1

Answer:

Q14. ( 5√3 - 4√2)/(4√3 + 3√2)

rationalising the denominator

(5√3 - 4√2) (4√3 - 3√2)

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(4√3 + 3√2) (4√3 - 3√2)

(5√3*4√3 - 5√3*3√2 - 4√2*4√3 + 4√2*3√2)

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((4√3)^2 - (3√2)^2)

(60 - 15√6 - 16√6 + 24)

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(48 - 18)

(84 - 31√6)/30

Q16). 6^(1/3),. 24^(1/6). 8^(1/4)

LCM of 3, 6 and 4 is 12

so we will make each exponent equal to 1/12. now,

6^(1/3) ^ 6^(1*4/(3*4)) = (6^4)^(1/12) = (1296)^(1/12)

24^(1/6) = 24^(1*2/(6*2)) = (24^2)^(1/12) = (576)^(1/12)

8^(1/4) = 8^(1*3/(4*3)) = (8^3)^(1/12) = (512)^(1/12)

now, since exponents are same

(512)^(1/12) < (576)^(1/12) < (1296)^(1/12)

8^(1/4) < (24)^(1/6) < 6^(1/3)

hence, 8^(1/4) is the smallest