Respuesta :

Answer:

[tex]2^{\frac{3}{2} }[/tex]

Step-by-step explanation:

note that 8 = 2³

and using the rule of exponents/ radicals

[tex]a^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{a^{m} }[/tex]

Thus

[tex]\sqrt{8}[/tex] = [tex]\sqrt{2^{3} }[/tex] = [tex]2^{\frac{3}{2} }[/tex]

Expressing the square root of 8 as a power of 2, we would have to follow two steps.

  • Step 1: We find the square root of 8

√8 = 2.8284271247

  • Step 2: We express the square root of 8 as a power of 2. We do this using the assumption method.

Assumption 1

[tex]2^{1}[/tex] = 2

Asumption 2

[tex]2^{1.2}[/tex]  =  2.29739671

Assumption 3

[tex]2^{1.5}[/tex]  = 2.8284271247

Therefore, the square of 8 as a power of 2 is [tex]2^{1.5}[/tex]

To learn more, visit the link below:

https://brainly.com/question/2142771

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