For this case we have:
By properties of the radicals [tex]\sqrt {a} = a ^{\frac {1} {2}}[/tex]
So:
[tex](\sqrt {7}) ^ 2 = (7 ^ {\frac {1} {2}}) ^ 2[/tex].
Now, for power properties we have:
[tex](b ^ {\frac {c} {d}}) ^ e = b ^ {\frac {c * e} {d}}[/tex]
Thus, [tex](7 ^ {\frac {1} {2}}) ^ 2 = 7 ^ {\frac {2} {2}} = 7[/tex]
So:
[tex]7 ^ {\frac {1} {2}} = \sqrt {7}[/tex]in its radical form
Answer:
[tex](\sqrt {7}) ^ 2 = (7 ^ {\frac {1} {2}}) ^ 2= 7 ^ {\frac {2} {2}} = 7[/tex] in its simplest form.
[tex]7 ^ {\frac {1} {2}} = \sqrt {7}[/tex]in its radical form
