Question

Which of the following expressions are equivalent to

Answer 1

Answer:

$(2^{6})^{\frac{1}{2} } , 4^{\frac{1}{2} } * 16^{\frac{1}{2} },8^{\frac{1}{2} } * 8^{\frac{1}{2}, \sqrt{16*4}$

Step-by-step explanation:

Some facts to establish before we try to solve: $\sqrt{64} =8$ and another way of writing $\sqrt{64}$ is $64^{\frac{1}{2} }$. 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 $64^{\frac{1}{2} }$, which is another way to write $\sqrt{64}$

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

$4^{\frac{1}{2} }* 16^{\frac{1}{2} }= \sqrt{4} *\sqrt{16} = 2*4=8$

Which is the same as $\sqrt{64}$

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

16*4= 64 and then $\sqrt{64}$

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