Order of Magnitude
 If x = √3 + √2, then the value of (x + 1)/(x  1)  (x  1)/(x + 1) is ?

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(x + 1)/(x  1)  (x  1)/(x + 1) = {(x + 1)^{2}  (x  1)^{2}} / {(x  1) (x + 1)}
= (x^{2} + 1 + 2x)  (x^{2} + 1  2x) / (x^{2}  1)
= 4x / (x^{2}  1) = 4(√3 + √2) / {(√3 + √2)^{2}  1}Correct Option: B
(x + 1)/(x  1)  (x  1)/(x + 1) = {(x + 1)^{2}  (x  1)^{2}} / {(x  1) (x + 1)}
= (x^{2} + 1 + 2x)  (x^{2} + 1  2x) / (x^{2}  1)
= 4x / (x^{2}  1) = 4(√3 + √2) / {(√3 + √2)^{2}  1}
= 4(√3 + √2) / (3 + 2 + 2√6  1) = 4(√3 + √2) / (4 + 2 √6)
= 4(√3 + √2) / 2 √2 (√3 + √2)
= √2
 Which among ∛8 and ∛1000 is greater ?

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∛8 and ∛1000 = 8^{1/3} and 1000^{1/3}
Correct Option: B
∛8 and ∛1000 = 8^{1/3} and 1000^{1/3}
Since 1000 > 8
∴ ∛1000 > ∛8
 Which among √81 and √1 is smaller ?

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√81 and √1 = 81^{1/2} and 1^{1/2}
Correct Option: B
√81 and √1 = 81^{1/2} and 1^{1/2}
Since, 1 < 81
∴ √1 < √81
 IF (14)^{3} is added to the square of a number, the answer to obtained is 4425. What is the number ?

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Let the number be x.
According to the question,
x^{2} + (14)^{3} = 4425Correct Option: C
Let the number be x.
According to the question,
x^{2} + (14)^{3} = 4425
⇒ x^{2} = 4425  (14)^{3}
⇒ x^{2} = 4425  2744
⇒ x^{2} = 1681
∴ x = √1681 = 41
 Which among ∜10 and ∛8 is greater ?

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∜10 and ∛8 = 10^{1/4} and 8^{1/3}
Since, LCM of 4 and 3 is 12.
∴ 10^{1/4} = 10^{3/12} = (10^{3})^{1/12} = (1000)^{1/12} = ^{12}√1000
and 8^{1/3} = 8^{4/12} = (8^{4})^{1/12} (4096)^{1/2} = ^{12}√4096
∴ 4096 > 1000Correct Option: B
∜10 and ∛8 = 10^{1/4} and 8^{1/3}
Since, LCM of 4 and 3 is 12.
∴ 10^{1/4} = 10^{3/12} = (10^{3})^{1/12} = (1000)^{1/12} = ^{12}√1000
and 8^{1/3} = 8^{4/12} = (8^{4})^{1/12} (4096)^{1/2} = ^{12}√4096
∴ 4096 > 1000
Hence, 8^{1/3} >10^{1/4}
∴ ∛8 > ∜10