Answer:
5 · a³ · b³ · √5b
Step-by-step explanation:
Start with √(50a^6b^7). Rewrite 50 as the product of the largest possible perfect square and a multiplier: 50 = 25 · 2. Then √50 = 5√2.
a^6 is already a perfect square, so find its square root: √a^6 = a^3.
b^7 = b · b^6, so √b^7 = b^3√b
Now rewrite (50(a^6) (b^7)) as √(50a^6b^7).
Then rewrite √(50a^6b^7) as 5√2 · a³ · b³ · √b.
This latter result can be simplified to 5 · a³ · b³ · √5b
This matches possible answer #1.
