Respuesta :

WojtekR
We have:

648 : 2 = 324 (even number)
324 : 2 = 162 (even number)
162 : 2 = 81 (odd number)
81 : 3 = 27 (odd number)
27 : 3 = 9 (odd number)
9 : 3 = 3 (odd number)
3 : 3 = 1

So a = 3 and b = 4 - answer C.

Answer:

Option (c) is correct.

a = 3 and b = 4

Step-by-step explanation:

Given : [tex]\sqrt{648}=\sqrt{2^a\cdot3^b}[/tex]  

We have to find the values of a and b and choose the correct options from the given options.

Consider [tex]\sqrt{648}[/tex]

We first factorize 648 that is writing 648  as products of its prime factors.

648  can be written as 8 × 81

breaking 8 as product of 2 and 81 as product of 3.

We get,

[tex]684=2^3\times 3^4[/tex]

Also,

[tex]\sqrt{648}=\sqrt{2^3\cdot3^4}[/tex]  

Thus, a = 3 and b = 4

Option (c) is correct.

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