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प्रश्न
Prove that:
`sqrt(1/4)+(0.01)^(-1/2)-(27)^(2/3)=3/2`
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उत्तर
We have to prove that `sqrt(1/4)+(0.01)^(-1/2)-(27)^(2/3)=3/2`
Let x = `sqrt(1/4)+(0.01)^(-1/2)-(27)^(2/3)`
`=sqrt(1/2^2)+((0.01xx100)/(1xx100))^(-1/2)-(3^3)^(2/3)`
`=1/2+1/(100)^(-1/2)-3^(3xx2/3)`
`=1/2+1/(1/100^(1/2))-3^2`
`=1/2+1/(1/(10xx10)^(1/2))-3^2`
`=1/2+1/(1/10^(2xx1/2))-3^2`
`=1/2+1/(1/10)-3^2`
`=1/2+1xx10/1-3xx3`
`=1/2+10-9`
`=3/2`
Hence, `sqrt(1/4)+(0.01)^(-1/2)-(27)^(2/3)=3/2`
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