Answer:
The simpler form of the radical expression [tex]\sqrt{36g^6}[/tex] is [tex]6g^3[/tex].
Step-by-step explanation:
To find the simpler form of the expression [tex]\sqrt{36g^6}[/tex].
Apply the radical rule [tex]\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0[/tex]
[tex]\sqrt{36}\sqrt{g^6}[/tex]
We have that [tex]\sqrt{36}=6[/tex], so [tex]\sqrt{36g^6}=6\sqrt{g^6}[/tex]
Next, apply the exponent rule [tex]a^{bc}=\left(a^b\right)^c[/tex]
[tex]g^6=g^{3\cdot \:2}=\left(g^3\right)^2[/tex]
[tex]\sqrt{36}\sqrt{g^6}=6\sqrt{\left(g^3\right)^2}[/tex]
Apply the radical rule [tex]\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]
[tex]\sqrt{\left(g^3\right)^2}=g^3[/tex]
Therefore,
[tex]\sqrt{36g^6}=6g^3[/tex]
