Question

if
${x}^{ \frac{1}{4 } } = m \: and \: {x}^{ \frac{1}{4} } = n$
and n=4m,then find the value of
$\sqrt{x}$

Answer 1

ANSWER
......
2178.
 
Let the number be abcdabcd.
 
abcd=1000a+100b+10c+dabcd=1000a+100b+10c+d

No need to say that a,b,ca,b,c and dd range from 0 to 9.
 
As per the problem:

4∗(abcd)=dcba4∗(abcd)=dcba   ...(1)

i.e.,
4000a+400b+40c+4d4000a+400b+40c


+4d =1000d+100c+10b+a=1000d+100c+10b+a

or

3999a+390b=996d+60c3999a+390b=996d+60c
 
To satisfy unit places of numbers

of both sides of equation

(1), a=2a=2 and d=8d=8 (and not 3,

as it won't give b and c from 0 to 9)
 
So finally we have,
 
1+13b=2c1+13b=2c
 
Since b and c are from 0 to 9

, the above equation is satisfied

only for b = 1 and c = 7. Hence the answer

is 2178
$= = = = = =$