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UNO [17]
2 years ago
11

Which rational exponent represents a square root? A. 1 / 2 B. 3/2 C. 1/3 D. 1/4

Mathematics
2 answers:
Vsevolod [243]2 years ago
6 0

Answer: A.) 1/2 is the correct answer

Step-by-step explanation:

Fofino [41]2 years ago
5 0

Answer:

1/2 rational exponent represents a square root.

Therefore, option A is correct.

Step-by-step explanation:

As we know that raising to the one-half power i.e. \frac{1}{2} is the same

as taking the square root.

  • so x^{\frac{1}{2}} is the same as the square root of x.

For example, taking the square root of 4 will determine:

4^{\frac{1}{2}}

\mathrm{Factor\:the\:number:\:}\:4=2^2

4^{\frac{1}{2}}=\left(2^2\right)^{\frac{1}{2}}

\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc},\:\quad \:a\ge 0

\left(2^2\right)^{\frac{1}{2}}=2^{2\cdot \frac{1}{2}}

so the expression becomes

4^{\frac{1}{2}}=2^{2\cdot \:\frac{1}{2}}

    =2^1

    =2         ∵ \mathrm{Apply\:exponent\:rule}:\quad \:a^1=a

so, 1/2 rational exponent represents a square root.

Therefore, option A is correct.

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