Answer:
D) [tex]6\sqrt{105}[/tex]
Step-by-step explanation:
The square root is a function that is distributed for the product and the division.
For example :
[tex](\sqrt{3}).(\sqrt{6})=\sqrt{(3).(6)}=\sqrt{18}[/tex]
First we need to factorize the numbers in the square roots ⇒
[tex]28=(2^{2}).(7)[/tex]
[tex]27=3^{3}[/tex]
[tex]5=5[/tex]
Now we replace this in the expression :
[tex]\sqrt{(2^{2}).(7)}\sqrt{3^{3}}\sqrt{5}[/tex]
Then we distribute the square root (remember that [tex]3^{3}=(3^{2}).(3)[/tex]
⇒
[tex]\sqrt{(2^{2}).(7)}\sqrt{(3^{2}).(3)}\sqrt{5}=\sqrt{2^{2}}\sqrt{7}\sqrt{3^{2}}\sqrt{3}\sqrt{5}[/tex]
This expression is equivalent to
[tex](2).(\sqrt{7}).(3)(\sqrt{3}).(\sqrt{5})=(6).\sqrt{7}\sqrt{3}\sqrt{5}=(6).\sqrt{(7).(3).(5)}=6\sqrt{105}[/tex]
Notice that in the last step we did the inverse operation.
The answer is D) [tex]6\sqrt{105}[/tex]
