IF (14) ³ is added to the square of a number, the answer to obtained is 4425. What is the number?

?81 and ?1 = 81^1/2 and 1^1/2
Since, 1 < 81
? ?1 < ?81

?8 and ?1000 = 8^1/3 and 1000^1/3
Since 1000 > 8
? ?1000 > ?8

(x + 1)/(x - 1) - (x - 1)/(x + 1) = {(x + 1)² - (x - 1)²} / {(x - 1) (x + 1)}
= (x² + 1 + 2x) - (x² + 1 - 2x) / (x² - 1)
= 4x / (x² - 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

Given that,
?16 + ?9.5 x 0.0085 x 18.9/0.021 x 0.0017 x 1.9
remove the decimal and simply the euqation.
= ?16 + ?95 x 85 x 18900/21 x 17 x 19
= 4 + ?5 x 5 x 900
= 4 + 5 x 30
= 4 + 150
= 154

Given that,
⁶?0.000729
first method to solve the equation.
after removing the decimal, the equation will be
= ⁶?729/1000000
Simplify the equation.
= ⁶?3 x 3 x 3 x 3 x 3 x 3 / 10 x 10 x 10 x 10 x 10 x 10
= ⁶?3⁶/10⁶
= ⁶?( 3/10 )⁶
After simplifying the root we will get,
= ( 3/10 )^{6 x 1/6}
= 3/10
= 0.3


Second method to solve the equation.
simplify the the number in multiplication of numbers.
⁶?0.000729
⁶?0.3 x 0.3 x 0.3 x 0.3 x 0.3 x 0.3
= ⁶?(0.3)⁶
remove the root and simplify ,
= (0.3)^{6 x 1/6}
= 0.3

?10 and ?8 = 10^1/4 and 8^1/3
Since, LCM of 4 and 3 is 12.
? 10^1/4 = 10^3/12 = (10³)^1/12 = (1000)^1/12 = ¹²?1000
and 8^1/3 = 8^4/12 = (8⁴)^1/12 (4096)^1/2 = ¹²?4096
? 4096 > 1000
Hence, 8^1/3 >10^1/4
? ?8 > ?10

74088 = 2 x 2 x 2 x 3 x 3 x 3 x 7 x 7 x 7
= (2 x 2) x (3 x 3) x (7 x 7) x ( 2 x 3 x 7)
? Least number which should be multiplied to 74088 to make it a perfect suqare = 2 x 3 x 7 = 42

Let the number be x.
Then, accordingto the question,
x² = (75.15)² - (60.12)²
? x² = 5647.52 - 3614.41
? x² = 2033.11
? x = 45.09

Let the total number of soliders in front be x. Then, total number of soliders in form of solid square = x²
According to the question, x² + 31 = 16160
? x² = 16129 ? x = ?16129
? x = 127

Let the total number of subbscribers be x.
Then, x² = 2582449
? x = ?2582449 = 1607