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Please Please please help me with this question! I'm so confused.

which is equivalent to square root of 5?

A) 5^2
B) 5^(-2)
C) 5^1/2
D) 5^(-1/2)

please show your wok.

User Cat Pants
by
7.1k points

2 Answers

3 votes
The answer is: [C]: " 5^(1/2) " .
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Step-by-step 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.
User Adrian Bob
by
8.2k points
5 votes
C because the square root of 5 is about 2.23606798 and 5 to the power of 1/2 is equal to 2.23606798. 
User Hong Jiang
by
8.1k points
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