Video Transcript
Calculate negative the square root
of 0.25.
In this question, we are asked to
evaluate the square root of a rational number given as a decimal. We can start by recalling that the
square root of 𝑎 is the nonnegative number whose square is 𝑎. We can then recall that it is
easier to find the square root of a rational number written as a fraction. So we rewrite 0.25 as one-quarter
to obtain negative the square root of one-quarter.
This then gives us two methods of
evaluating the square root. Either we can note that one-half
squared is one-quarter or we can use the quotient rule for square roots, which tells
us that if 𝑎 and 𝑏 are integers with 𝑎 nonnegative and 𝑏 positive, then the
square root of 𝑎 over 𝑏 is equal to the square root of 𝑎 over the square root of
𝑏. We can apply this result with 𝑎
equal to one and 𝑏 equal to four to get negative the square root of one over the
square root of four.
Finally, we can see that the
numerator is the same as the square root of one squared and the denominator is the
same as the square root of two squared. Therefore, we can evaluate the
roots to obtain negative one-half.
We can check our answer by
multiplying one-half by one-half to see that we get one-quarter, which is 0.25. So one-half is the square root of
0.25. Hence, negative the square root of
0.25 is negative one-half.
