how to find cuberoot of non-perfect square. example ³√2,³√4
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Step-by-step explanation:
let, m be integer and a non perfect square.
By taking log and antilog
Let y=m^1/3
Taking log both sides
log y = log (m^1/3)
log y= (1/3)logm ——[log(a^b)=(b)log(a)]
(1/3)logm is an constant.
so,
by taking antilog both sides we will get the answer.
Example:-
⚫By taking log and antilog
Let y=2^1/3
Taking log both sides
log y = log (2^1/3)
log y= (1/3)log2 ——[log(a^b)=(b)log(a)]
log y=(1/3)0.3010 ———-[log 2=0.3010]
log y= 0.1003
Taking antilog both sides
y= 1.2598
⚫By taking log and antilog
Let y=4^1/3=2^(2/3)
Taking log both sides
log y = log (2^2/3)
log y= (2/3)log2 ——[log(a^b)=(b)log(a)]
log y=(2/3)0.3010 ———-[log 2=0.3010]
log y= 0.2006
Taking antilog both sides
y=1.587
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