The simplest radical form is [tex]2 \sqrt{17}[/tex]
Explanation:
The expression is [tex]\sqrt{68}[/tex]
To determine the radical form, let us write the number 68 as a product of prime factors.
Thus, we have,
[tex]\sqrt{68} =\sqrt{2\times2\times17}[/tex]
Since, 2, 17 are prime factors and hence, no further factorization is possible.
Hence, it can be written as,
[tex]\sqrt{68} =\sqrt{2^{2} \times17}[/tex]
Applying the radical rule [tex]\sqrt{a b}=\sqrt{a} \ \sqrt{b}[/tex], we have,
[tex]\sqrt{68} =\sqrt{2^{2}} \sqrt{17}[/tex]
Simplifying, we have,
[tex]\sqrt{68} =2 \sqrt{17}[/tex]
Thus, the simplest radical form is [tex]2 \sqrt{17}[/tex]
