Answer:
[tex](2^{6})^{\frac{1}{2} } , 4^{\frac{1}{2} } * 16^{\frac{1}{2} },8^{\frac{1}{2} } * 8^{\frac{1}{2}, \sqrt{16*4}[/tex]
Step-by-step explanation:
Some facts to establish before we try to solve: [tex]\sqrt{64} =8[/tex] and another way of writing [tex]\sqrt{64}[/tex] is [tex]64^{\frac{1}{2} }[/tex]. 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 [tex]64^{\frac{1}{2} }[/tex], which is another way to write [tex]\sqrt{64}[/tex]
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:
[tex]8^{2} *8^{2} = 64 * 64=[/tex]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
[tex]4^{\frac{1}{2} }* 16^{\frac{1}{2} }= \sqrt{4} *\sqrt{16} = 2*4=8[/tex]
Which is the same as [tex]\sqrt{64}[/tex]
Fifth: Like the third, we solve the inside of the square root first
16*4= 64 and then [tex]\sqrt{64}[/tex]
Sixth: We need a nice whole number (8), and [tex]\sqrt{32}[/tex] has no clean roots, so its result will have decimals. It can't be our answer
