Video Transcript
Fill in the blank. 21 times the square root of two is
equal to what times 21.
In this question, we are asked to
fill in the blank in an equation. To do this, we can start by noting
that both sides of the equation are a product of real numbers and the factor of 21
has been reordered. Since this involves the reordering
of the multiplication of real numbers, this should remind us of the commutativity of
the multiplication of real numbers, which tells us that for any real numbers 𝑎 and
𝑏, we have that 𝑎 times 𝑏 is equal to 𝑏 times 𝑎. If we set 𝑎 equal to 21 and 𝑏
equal to the square root of two in this property, then we obtain that 21 times the
square root of two is equal to the square root of two times 21.
Hence, by the commutativity of the
multiplication of real numbers, we can switch the order of the product on the
left-hand side of the equation to get the square root of two times 21.
