Question

1. rosa is considering $sqrt{7}$ and 3.44444. she says that $sqrt{7}=3.44444$, meaning $sqrt{7}=3.4$.a. what is the correct comparison?b. critique reasoning what mistake did rosa likely make?15. higher order thinking the length of a rectangle is twice the width. the area of the rectangle is 90 square units. note that you can divide the rectangle into two squares.a. which irrational number represents the length of each side of the squares?b. estimate the length and width of the rectangle.18. model with math approximate $sqrt{2.3}$ to the nearest tenth. plot the point on the number line.assessment practice16. which list shows the numbers in order from least to greatest?a $-4, -\frac{9}{4}, \frac{1}{2}, 3.7, sqrt{5}$b $-4, -\frac{9}{4}, \frac{1}{2}, sqrt{5}, 3.7$c $-\frac{9}{4}, \frac{1}{2}, 3.7, sqrt{5}, -4$d $-\frac{9}{4}, -4, \frac{1}{2}, 3.7, sqrt{5}$17. the area of a square poster is 31 square inches. find the length of one side of the poster. explain.part ato the nearest whole inchpart bto the nearest tenth of an inch

Explanation:

Question 14

Step1: Calculate $3.4444^2$

$3.4444^2 = 3.4444\times3.4444 \approx 11.863$

Step2: Compare to $\sqrt{7}$

First, $\sqrt{7} \approx 2.6458$, so $\sqrt{7} < 3.4444$

Step3: Identify Rosie's mistake

Rosie assumed $\sqrt{7}=3.4444$ but $3.4444^2
eq7$, she confused the value.

Step1: Define rectangle variables

Let width $w$, length $l=2w$. Area $A=l\times w=90$

Step2: Solve for width

Substitute $l=2w$: $2w\times w=90 \implies 2w^2=90 \implies w^2=45 \implies w=\sqrt{45}=3\sqrt{5}\approx6.708$

Step3: Find length

$l=2w=2\times3\sqrt{5}=6\sqrt{5}\approx13.416$

Step4: Square side length

The rectangle divides into 2 squares, so square side = $w\approx6.708$ (rational approximation: $\frac{45}{7}\approx6.428$ or exact $\sqrt{45}$ simplified to $3\sqrt{5}$, but rational number: $\frac{90}{13}\approx6.923$ or the rational approximation of $\sqrt{45}$ is $\frac{671}{100}$)

Step1: Convert all to decimals

$-4=-4$, $-\frac{9}{4}=-2.25$, $\frac{1}{2}=0.5$, $3.7=3.7$, $\sqrt{5}\approx2.236$

Step2: Order from least to greatest

$-4 < -2.25 < 0.5 < 2.236 < 3.7$

Answer:

a. $\boldsymbol{\sqrt{7} < 3.4444}$
b. Rosie incorrectly assumed $\sqrt{7}$ equals 3.4444, but squaring 3.4444 gives a value much larger than 7, so she misidentified the square root.

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Question 15