Question

Which of the following expressions are equivalent to

Answer 1

`(2^(6))^{(1)/(2) } , 4^{(1)/(2) } * 16^{(1)/(2) },8^{(1)/(2) } * 8^{(1)/(2), √(16*4)`

Explanation:

Some facts to establish before we try to solve:
`√(64) =8` and another way of writing
`√(64)` is
`64^{(1)/(2) }`. Also order of operations: PEMDAS

For the first option:

We solve what is in the parenthesis: 2*2=4*2=8*2=16*2=32*2=64 so
`64^{(1)/(2) }`, which is another way to write
`√(64)`

For the second option: If the square root of 64 is 8, the there is no way we can multiply another value by it.

The third option: When dealing with square roots, we can solve the inside first and then take the square root:

`8^(2) *8^(2) = 64 * 64=`definitely not 64 (though if you're curious it's 4096)

The fourth: Another way to write the square root is to raise the value to the 1/2 power so

`4^{(1)/(2) }* 16^{(1)/(2) }= √(4) *√(16) = 2*4=8`

Which is the same as
`√(64)`

Fifth: Like the third, we solve the inside of the square root first

16*4= 64 and then
`√(64)`

Sixth: We need a nice whole number (8), and
`√(32)` has no clean roots, so its result will have decimals. It can't be our answer