Calculate positive or negative the
square root of three and 61 over 100.
In this question, we are asked to
calculate the value of an expression. And there are two things that we
can start by noting. First, the expression starts with a
positive or negative symbol. This means that we will obtain two
values: one when we use the positive value and another when we use the negative
value. Second, we can see that we are
taking the square root of a mixed number. To calculate this root, we first
need to rewrite the mixed number as a fraction. And we can do this by rewriting
three as 300 over 100. We see that three and 61 over 100
is equal to 361 over 100. Therefore, we can rewrite the
expression that we are asked to evaluate as positive or negative the square root of
361 over 100.
We can now see that we want to
evaluate the square root of a rational number. And to do this, we can recall the
quotient rule for square roots. This tells us that if 𝑎 and 𝑏 are
integers with 𝑎 greater than or equal to zero 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 to our
expression, with 𝑎 equal to 361 and 𝑏 equal to 100, to obtain positive or negative
the square root of 361 over the square root of 100.
We can simplify this expression
further by noting that 361 is equal to 19 times 19 and 100 is equal to 10 times
10. So we can rewrite our expression as
positive or negative the square root of 19 squared over the square root of 10
Finally, we can recall that if 𝑐
is nonnegative, then the square root of 𝑐 squared is just equal to 𝑐. We can apply this to each of the
square roots to get positive or negative 19 over 10. Hence, we have shown that positive
or negative the square root of three and 61 over 100 is equal to either 19 over 10
or negative 19 over 10.