Please answer the following question step by step
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Given :-
³√(0.512/y) = ³√1000
To find :-
Find the value of y ?
Solution :-
Given that:
³√(0.512/y) = ³√1000
Since nth root a = a^1/n
=> (0.512/y)^1/3 = (1000)^1/3
On cubing both sides then
=> [(0.512/y)^1/3 ]³= [(1000)^1/3]³
=> (0.512/y)^3/3 = (1000)^3/3
Since (a^m)^n = a^mn
=> 0.512/y = 1000
=> 0.512 = 1000×y
=> 1000×y = 0.512
=> 1000×y = 512/1000
=> y = (512/1000)/1000
=> y = 512/(1000×1000)
=> y = 512/1000000
=> y = 0.000512
Therefore, y = 0.000512
Answer:-
The value of y for the given problem is 0.000512
Check:-
If y = 0.000512 then
LHS = ³√(0.512/y)
=> ³√(0.512/0.000512)
=> ³√[(512/1000)/(512/1000000)]
=> ³√(1000000/1000)
=> ³√1000
=> RHS
=> LHS = RHS is true for y = 0.000512
Check :-
- (a^m)^n = a^mn
- nth root a = a^1/n
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I think the following ll b the answer...
y = (2/25)^3 or 8/15625 or 0.000512
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