Complete the following: The fourth
root of 16 equals the square root of blank.
In this question, on the right-hand
side, we have a value which is taken to the square root, and we know that it’s equal
to the fourth root of 16. Let’s therefore begin by working
out the fourth root of 16. But first, a note, this is not the
same as four multiplied by the square root of 16. We can tell the difference by
looking at the size of the digits. For example, when we’re working out
four multiplied by the square root of 16, the four and the 16 should be the same
size. However, when we’re taking an 𝑛th
root, for example, the fourth root here, the four will be smaller and usually set
within the root sign.
So in order to actually calculate
the fourth root of 16, it’s equivalent to thinking that there’s a value 𝑥 written
to the fourth power, which would give us an answer of 16. 𝑥 to the fourth power is 𝑥
written four times and multiplied together. If we tried the value of 𝑥 equals
two, we’d need to work out two times two times two times two, and two times two is
four. Four multiplied by the third two
would give us eight. And eight multiplied by the final
two would give us 16. Therefore, two to the fourth power
is 16. And importantly for us, that means
that the fourth root of 16 is two.
However, when we look back at the
original question, we can’t just fill in the value two onto the blank because it’s
this whole expression on the right-hand side that needs to be equal to two. Therefore, we need to think about
what value would give us an answer of two when we take the square root of it. Well, two squared would give us
four. And therefore, the square root of
four would give us two. We can therefore give our answer
that the missing value is four since the fourth root of 16 is equal to the square
root of four.