Respuesta :
C because the square root of 5 is about 2.23606798 and 5 to the power of 1/2 is equal to 2.23606798.
The answer is: [C]: " 5^(1/2) " .
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Explanation:
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The square root of 5 is expressed as:
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√5 .
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Note: The cubic root of 5 would be expressed as:
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∛5 .
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So, the "square root of 5" is actually:
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²√5 . By convention, for "square roots", we eliminate
"superscript 2".
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Also, note that: √5 = ²√5 = ²√(5¹) ;
Since "5¹ = 5" ;
By convention we often eliminate the "{raised to the power of 1}" .
So, √5 = ²√5 = ²√(5¹) = 5^(1/2) ;
Thus, √5 = 5^(1/2) ;
In the "(1/2)" power, the "1" comes from the [implied exponent]
of "1" in " 5¹ " ; and the "2" comes from the "square
root".
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Note that "5^(3/2) = ²√(5³) = √(5³) = √(5*5*5) = √5* √5 *√5 = 5√5 .
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Note that "6^(4/3) = ∛ (6⁴).
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A bit too lengthy, but hope this explanation helps.
__________________________________________
Explanation:
__________________________________________
The square root of 5 is expressed as:
_________________________________________
√5 .
_________________________________________
Note: The cubic root of 5 would be expressed as:
_________________________________________
∛5 .
_________________________________________
So, the "square root of 5" is actually:
_________________________________________
²√5 . By convention, for "square roots", we eliminate
"superscript 2".
_______________________________________________
Also, note that: √5 = ²√5 = ²√(5¹) ;
Since "5¹ = 5" ;
By convention we often eliminate the "{raised to the power of 1}" .
So, √5 = ²√5 = ²√(5¹) = 5^(1/2) ;
Thus, √5 = 5^(1/2) ;
In the "(1/2)" power, the "1" comes from the [implied exponent]
of "1" in " 5¹ " ; and the "2" comes from the "square
root".
_________________________________________________________
Note that "5^(3/2) = ²√(5³) = √(5³) = √(5*5*5) = √5* √5 *√5 = 5√5 .
_____________________________________________________
Note that "6^(4/3) = ∛ (6⁴).
_____________________________________________________
A bit too lengthy, but hope this explanation helps.
