Question

1. the table shows the side length and area of several different squares. complete the table using exact values.

side length (cm) 5 $sqrt{7}$ $sqrt{63}$ $sqrt{125}$
area ($cm^{2}$) 49 98 102

1. find the two whole numbers that are the closest to $sqrt{42}$. explain your reasoning.

Explanation:

For Question 4:

Step1: Calculate area for side=5

Area of square = side², so $5^2 = 25$

Step2: Find side for area=49

Side = $\sqrt{\text{area}}$, so $\sqrt{49} = 7$

Step3: Calculate area for side=$\sqrt{63}$

Area = $(\sqrt{63})^2 = 63$

Step4: Find side for area=98

Side = $\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}$

Step5: Find side for area=102

Side = $\sqrt{102}$

Step6: Calculate area for side=$\sqrt{125}$

Area = $(\sqrt{125})^2 = 125$

Identify perfect squares around 42. $6^2=36$ and $7^2=49$. 42 is between 36 and 49, and $|42-36|=6$, $|49-42|=7$, so 6 and 7 are the closest whole numbers.

Answer:

side length (cm)	5	7	$\sqrt{63}$	$7\sqrt{2}$	$\sqrt{102}$	$\sqrt{125}$

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For Question 5: