Question

match each number to the letter that represents its relative position on the number line.

1. $\frac{23}{2}$
2. $sqrt{\frac{484}{4}}$
3. $sqrt{160}$
4. 11.75

(the spaces between tick marks on the number line are not to scale.)

1. $\frac{23}{2}$ corresponds to position
2. $sqrt{\frac{484}{4}}$ corresponds to position
3. $sqrt{160}$ corresponds to position
4. 11.75 corresponds to position

Explanation:

24. $\boldsymbol{\frac{23}{2}}$

Step1: Calculate the value

$\frac{23}{2}=11.5$

Step2: Analyze position

We'll compare with other values later, but first, note this is 11.5.

25. $\boldsymbol{\sqrt{\frac{484}{4}}}$

Step1: Simplify the fraction

$\frac{484}{4} = 121$

Step2: Take the square root

$\sqrt{121}=11$

26. $\boldsymbol{\sqrt{160}}$

Step1: Estimate the square root

We know that $12^2 = 144$ and $13^2 = 169$. So $\sqrt{160}$ is between 12 and 13, closer to 12 (since $12.6^2=158.76$ and $12.7^2 = 161.29$), so $\sqrt{160}\approx12.65$

27. $\boldsymbol{11.75}$

Answer:

1. $\frac{23}{2}$ corresponds to position B
2. $\sqrt{\frac{484}{4}}$ corresponds to position A
3. $\sqrt{160}$ corresponds to position D
4. $11.75$ corresponds to position C