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Which of the following is equal to sqrt. (50(a^6) (b^7))

Which of the following is equal to sqrt. (50(a^6) (b^7))-example-1

1 Answer

2 votes

Answer:

5 · a³ · b³ · √5b

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.

User Elman Huseynov
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