Video Transcript
Evaluate negative the square root of 0.000169.
In this question, we are asked to evaluate an expression involving the square root of a rational number given as a decimal. To do this, we can start by recalling that it is usually easier to evaluate square roots of rational numbers given as fractions. We can calculate that multiplying the radicand by one million gives us 169. So, we can rewrite the expression as negative the square root of 169 over one million.
We can then evaluate the square root by recalling 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 to our expression with 𝑎 equal to 169 and 𝑏 equal to one million to obtain negative the square root of 169 over the square root of one million.
We can simplify the expression by noting that we are taking the square roots of perfect squares. In particular, 169 is equal to 13 squared and one million is equal to 1,000 squared. This allows us to evaluate both square roots by recalling that if 𝑎 is nonnegative, then the square root of 𝑎 squared is equal to 𝑎.
So, the square root of 169 is 13 and the square root of one million is 1,000, giving us negative 13 over 1,000. We can rewrite this fraction as a decimal to find that negative the square root of 0.000169 is equal to negative 0.013.
