Question

problem 15:
tell which of these numbers is greater. (use estimates for the irrationals.)
after you enter your answer press go.
a. $-sqrt{5}$ b. $-sqrt{2}$

Explanation:

Step1: Estimate square roots

We know that $\sqrt{4} = 2$ and $\sqrt{9}=3$, so $\sqrt{5}$ is between 2 and 3 (since $4<5<9$), and more precisely, $\sqrt{5}\approx 2.24$. Also, $\sqrt{1} = 1$ and $\sqrt{4}=2$, so $\sqrt{2}$ is between 1 and 2, and $\sqrt{2}\approx 1.41$.

Step2: Analyze negative square roots

For negative numbers, the larger the absolute value, the smaller the number. So we find the absolute values of $-\sqrt{5}$ and $-\sqrt{2}$. The absolute value of $-\sqrt{5}$ is $\sqrt{5}\approx 2.24$, and the absolute value of $-\sqrt{2}$ is $\sqrt{2}\approx 1.41$. Since $2.24>1.41$, then $-\sqrt{5}<-\sqrt{2}$ (because when dealing with negative numbers, a larger absolute value means a smaller number). So $-\sqrt{2}$ (option B) is greater than $-\sqrt{5}$ (option A).

Answer:

B. $-\sqrt{2}$