Which choices are equivalent to the expression below? check all that apply.4√(6)a. √(96)b.√(24)c. 96d. √(4) * √(36)e.√(16) * √(6)f.√(32) * √(3)

Question

which choices are equivalent to the expression below? check all that apply.
`4√(6)`a.
`√(96)`b.
`√(24)`c. 96d.
`√(4) * √(36)`e.
`√(16) * √(6)`f.
`√(32) * √(3)`

Answer 1

To find the equivalents of this expression we can write it another way:

`4\cdot\sqrt[]{6}=\sqrt[]{16\cdot6}=\sqrt[]{4\cdot4\cdot6}=\sqrt[]{2\cdot2\cdot2\cdot2\cdot2\cdot3}`

We can group the 2's and 3 however we want and the expression will be the same.

If we do the multiplication of all of them (or 16 times 6, is the same) we get that it's 96, so option a is one equivalent

`\sqrt[]{96}`

Then from the second term we have that another equivalent is

`\sqrt[]{16}\cdot\sqrt[]{6}`

Because the square root can be distributed into the product. So option e is equivalent

If we multiply all the 2's we get that it's 32, so another equivalent is:

`\sqrt[]{32}\cdot\sqrt[]{3}`

Option f is equivalent