Answer :
We start with the expression
[tex]$$12\sqrt{17} - 8\sqrt{17}.$$[/tex]
Notice that both terms contain the common factor [tex]$\sqrt{17}$[/tex]. This allows us to factor it out:
[tex]$$
12\sqrt{17} - 8\sqrt{17} = (12 - 8)\sqrt{17}.
$$[/tex]
Now, subtract the coefficients:
[tex]$$12 - 8 = 4.$$[/tex]
So, the expression simplifies to:
[tex]$$
(12 - 8)\sqrt{17} = 4\sqrt{17}.
$$[/tex]
If we evaluate this numerically, we find that
[tex]$$\sqrt{17} \approx 4.123105625617661,$$[/tex]
thus
[tex]$$
4\sqrt{17} \approx 4 \times 4.123105625617661 \approx 16.492422502470644.
$$[/tex]
Therefore, the final result is
[tex]$$\boxed{4\sqrt{17} \approx 16.49242250247064.}$$[/tex]
[tex]$$12\sqrt{17} - 8\sqrt{17}.$$[/tex]
Notice that both terms contain the common factor [tex]$\sqrt{17}$[/tex]. This allows us to factor it out:
[tex]$$
12\sqrt{17} - 8\sqrt{17} = (12 - 8)\sqrt{17}.
$$[/tex]
Now, subtract the coefficients:
[tex]$$12 - 8 = 4.$$[/tex]
So, the expression simplifies to:
[tex]$$
(12 - 8)\sqrt{17} = 4\sqrt{17}.
$$[/tex]
If we evaluate this numerically, we find that
[tex]$$\sqrt{17} \approx 4.123105625617661,$$[/tex]
thus
[tex]$$
4\sqrt{17} \approx 4 \times 4.123105625617661 \approx 16.492422502470644.
$$[/tex]
Therefore, the final result is
[tex]$$\boxed{4\sqrt{17} \approx 16.49242250247064.}$$[/tex]
