Question

1. simplify:

$sqrt{144}$ ____ $sqrt{361}$ ____
$-sqrt{144}$ ____ $-sqrt{49}$ ____
$-sqrt{1}$ ____ $-sqrt{225}$ ____

1. simplify each expression:

$3sqrt{49} = $ ______
$\frac{sqrt{576}}{8} = $ ______
$sqrt{121} - 4 = $ ______

1. which best describes $sqrt{35}$?

a. exactly 5 c. between 5 and 6
b. exactly 17.5 d. between 31 and 37

1. circle all numbers that lie between $2.8\times10^0$ and $sqrt{12.25}$

3\\%, $\frac{11}{3}$, 3.6, 2.8, $sqrt{13}$, 294\\%, $3.5\times10^1$

1. selecting a queen from a deck of cards, keeping it and then selecting a heart.

independent events or dependent events

1. a chorus class has 50 8th graders and 35 7th graders. two students are selected at random to sing a duet. what is the probability that both are 7th graders (without replacement)?

$p(7^{\text{th}} \text{ grader}, 7^{\text{th}} \text{ grader})$

1. when ordering from least to greatest, which number would come first?

$7.5\times10^{-1}$, $70\\%$, $\frac{7}{100}$, $0.0075$

1. plot the $sqrt{113}$ on the number line.

number line diagram
what whole number is $sqrt{113}$ closest to on the number line?

Explanation:

Problem 7: Simplify the square roots

$\boldsymbol{\sqrt{144}}$

Step1: Recall square of 12

We know that $12\times12 = 144$. So, by the definition of square root, $\sqrt{144}$ is the number whose square is 144.
$\sqrt{144}=12$

$\boldsymbol{\sqrt{361}}$

Step1: Recall square of 19

We know that $19\times19 = 361$. So, by the definition of square root, $\sqrt{361}$ is the number whose square is 361.
$\sqrt{361}=19$

$\boldsymbol{-\sqrt{144}}$

Step1: Find $\sqrt{144}$ first

We already found that $\sqrt{144}=12$. Then, applying the negative sign, we get $-\sqrt{144}=- 12$

$\boldsymbol{-\sqrt{49}}$

Step1: Recall square of 7

We know that $7\times7 = 49$. So, $\sqrt{49}=7$. Then, applying the negative sign, we get $-\sqrt{49}=-7$

$\boldsymbol{-\sqrt{1}}$

Step1: Recall square of 1

We know that $1\times1 = 1$. So, $\sqrt{1}=1$. Then, applying the negative sign, we get $-\sqrt{1}=-1$

$\boldsymbol{-\sqrt{225}}$

Step1: Recall square of 15

We know that $15\times15 = 225$. So, $\sqrt{225}=15$. Then, applying the negative sign, we get $-\sqrt{225}=-15$

Problem 8: Simplify each expression

$\boldsymbol{3\sqrt{49}}$

Step1: Find $\sqrt{49}$

We know that $7\times7 = 49$, so $\sqrt{49}=7$.

Step2: Multiply by 3

Now, multiply 3 with 7: $3\times7 = 21$
$3\sqrt{49}=21$

$\boldsymbol{\frac{\sqrt{576}}{8}}$

Step1: Find $\sqrt{576}$

We know that $24\times24 = 576$, so $\sqrt{576}=24$.

Step2: Divide by 8

Now, divide 24 by 8: $\frac{24}{8}=3$
$\frac{\sqrt{576}}{8}=3$

$\boldsymbol{\sqrt{121}-4}$

Answer:

c. between 5 and 6

Problem 10: Circle all numbers that lie between $\boldsymbol{2.8\times10^{0}}$ and $\boldsymbol{\sqrt{12.25}}$

First, simplify the bounds:

• $2.8\times10^{0}=2.8\times1 = 2.8$
• $\sqrt{12.25}=3.5$ (since $3.5\times3.5 = 12.25$)

Now, check each number:

• $3\%=0.03$: $0.03<2.8$, so no.
• $\frac{11}{3}\approx3.67$: $3.67 > 3.5$, so no.
• $3.6$: $3.6>3.5$, so no.
• $2.8$: equal to the lower bound, if we consider "between" as strictly between, then no. But if inclusive, it is. But let's check others.
• $\sqrt{13}\approx3.605$: $3.605>3.5$, so no.
• $294\% = 2.94$: $2.8<2.94<3.5$, so yes.
• $3.5\times10^{1}=35$: $35>3.5$, so no.
• $0.03$: as above, no.

So the number that lies between $2.8$ and $3.5$ is $294\%$ (or $2.94$)

Problem 11: Selecting a queen from a deck of cards, keeping it and then selecting a heart. Independent or Dependent?