Final answer:
The simplified form of the radical expression √36g⁶ is 6g³, obtained by taking the square root of 36, which is 6, and the square root of g⁶, which is g³.
Step-by-step explanation:
The question asks for the simplified form of the radical expression √36g⁶. To simplify a radical expression involving a perfect square and even powers, we can take the square root of each factor separately. The square root of 36 is 6, and the square root of g to the sixth power is g cubed since raising g to the sixth power and then taking the square root is the same as raising g to the power of 6/2, which simplifies to 3.
The given expression is √36g⁶. To find a simpler form of this expression, we can simplify the square root of 36 and simplify the exponent of g.
Since the square root of 36 is 6, we can rewrite the expression as 6g⁶.
This is the simpler form of the radial expression √36g⁶.
Therefore, the simplified form of √36g⁶ is 6g³.