Video Transcript
Calculate the square root of 53
multiplied by the square root of 53.
In this question, we are asked to
evaluate an expression involving the product of two square roots of the same
number. The easiest way to evaluate this
expression is to recall that for any nonnegative real number 𝑎, the square root of
𝑎 times the square root of 𝑎 is equal to 𝑎. Therefore, if we set 𝑎 equal to
53, we get that root 53 times root 53 is equal to 53.
This is enough to answer the
question. However, it can be useful to see
where this result comes from using this example. We can first recall that the square
root of 53 means the nonnegative number whose square is 53. We know that this number is real
because 53 is nonnegative. This means that if we say that the
square root of 53 is equal to 𝑏, then we must have that 𝑏 squared is 53.
But remember, 𝑏 is the square root
of 53, so we can substitute this into the equation. This gives us that the square root
of 53 squared is equal to 53. We can then write this product out
in full. This gives us that the square root
of 53 times the square root of 53 is equal to 53. This method holds true for the
square root of any nonnegative real number, proving our result of root 𝑎 times root
𝑎 equals 𝑎, provided 𝑎 is nonnegative.
Hence, the answer to this question
is that root 53 times root 53 is equal to 53.
