Advertisements
Advertisements
Question
If \[\sqrt{5^n} = 125\] then `5nsqrt64`=
Options
25
\[\frac{1}{125}\]
625
\[\frac{1}{5}\]
Advertisements
Solution
We have to find `5nsqrt64` provided \[\sqrt{5^n} = 125\]
So,
`sqrt 5^n = 125`
`5^(nxx 1/2)= 5^3`
`n/2 = 3`
`n=3xx2`
` n =6`
Substitute ` n =6` in `5nsqrt64` to get
` `5nsqrt64 = 5^(2^(6x1/6)`
=` 5^(2^(6x1/6)`
`= 5xx5`
`=25`
Hence the value of `5nsqrt64` is 25.
APPEARS IN
RELATED QUESTIONS
Find:-
`64^(1/2)`
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrt(x^-3))^5`
If `a=x^(m+n)y^l, b=x^(n+l)y^m` and `c=x^(l+m)y^n,` Prove that `a^(m-n)b^(n-l)c^(l-m)=1`
If 24 × 42 =16x, then find the value of x.
The product of the square root of x with the cube root of x is
If x-2 = 64, then x1/3+x0 =
The value of m for which \[\left[ \left\{ \left( \frac{1}{7^2} \right)^{- 2} \right\}^{- 1/3} \right]^{1/4} = 7^m ,\] is
If x is a positive real number and x2 = 2, then x3 =
The value of 64-1/3 (641/3-642/3), is
If o <y <x, which statement must be true?
