Question

Which choices are equivalent to the expression below? Check all that apply.

4√6
a. √4.√36
b. √32.√3
c. √16.6
d. √24
e. √96
f. 96

Answer 1

Options (b), (c), and (e) are equivalent to the expression 4√6. They simplify to the same numerical value when the square roots and multiplications are carried out, unlike the other options provided.

Step-by-step explanation:

To find which choices are equivalent to the expression 4√6, we need to find expressions that when simplified will result in the same value as 4√6.

The given expression 4√6 can be rewritten using properties of exponents and roots as (4²)¹⁄₂ × (6¹)¹⁄₂, which is equivalent to √(4² × 6) or √96.

• Option (a) √4.√36 simplifies to 2⋅√36 which equals 2⋅6. This is not equivalent to 4√6.
• Option (b) √32.√3 simplifies to √(32⋅3) which equals √96. This is equivalent to 4√6.
• Option (c) √16.6 simplifies to √(16⋅6) which equals √96. This is equivalent to 4√6.
• Option (d) √24 does not simplify to √96 and therefore is not equivalent to 4√6.
• Option (e) √96 is already in the required form and is equivalent to 4√6.
• Option (f) 96 is not equivalent to 4√6 because it does not involve a square root.