Question

1. select true or false for each statement:

a. √63 is between 6 and 7? ⃝ true ⃝ false
b. 2√8 is between 5 and 6? ⃝ true ⃝ false
c. 5√3 is between 8 and 9? ⃝ true ⃝ false
d. √3 is between 1 and 2? ⃝ true ⃝ false
e. 3√15 is between 12 and 13? ⃝ true ⃝ false

1. which expression is less than 4π? circle all that apply.

a. √14
b. 4e
c. √19
d. 3√2
e. √24

1. is the number between 4 and 5? select yes/no for each:

a. 3√2 ⃝ no ⃝ yes
b. 2√9 ⃝ no ⃝ yes
c. (1/3)√80 ⃝ no ⃝ yes
d. √17 ⃝ no ⃝ yes
e. 2√7 ⃝ no ⃝ yes

1. look at each square root. which are irrational? circle all that apply.

a. √10
b. √12
c. √16
d. √36
e. √49
f. √24

Explanation:

Question 8 (True/False for each statement)

Part A: $\boldsymbol{\sqrt{50}}$ between 6 and 7?

Step1: Find squares around 50

We know that $6^2 = 36$ and $7^2 = 49$. But $50>49$, so $\sqrt{50}>\sqrt{49} = 7$. So it's not between 6 and 7.

Step2: Conclusion

So the statement is False.

Part B: $\boldsymbol{2\sqrt{8}}$ between 5 and 6?

Step1: Simplify $2\sqrt{8}$

First, $\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}\approx2\times1.414 = 2.828$. Then $2\sqrt{8}=2\times2.828 = 5.656$.

Step2: Check range

5.656 is between 5 and 6. So the statement is True.

Part C: $\boldsymbol{5\sqrt{3}}$ between 8 and 9?

Step1: Calculate $5\sqrt{3}$

$\sqrt{3}\approx1.732$, so $5\sqrt{3}=5\times1.732 = 8.66$.

Step2: Check range

8.66 is between 8 and 9. So the statement is True.

Part D: $\boldsymbol{\sqrt{3}}$ between 1 and 2?

Answer:

Step1: Calculate $3\sqrt{15}$

$\sqrt{15}\approx3.872$, so $3\sqrt{15}=3\times3.872 = 11.616$.

Step2: Check range

11.616 is less than 12, so not between 12 and 13. So the statement is False.

Question 9 (Which expression is less than 4π? Circle all that apply)

First, calculate $4\pi\approx4\times3.1416 = 12.566$. Now check each option:

• Option A: $\boldsymbol{\sqrt{14}}$

$\sqrt{14}\approx3.742<12.566$.

• Option B: $\boldsymbol{4e}$

$e\approx2.718$, so $4e\approx10.872<12.566$.

• Option C: $\boldsymbol{\sqrt{19}}$

$\sqrt{19}\approx4.359<12.566$.

• Option D: $\boldsymbol{3\sqrt{2}}$

$\sqrt{2}\approx1.414$, so $3\sqrt{2}\approx4.242<12.566$.

• Option E: $\boldsymbol{\sqrt{24}}$

$\sqrt{24}\approx4.899<12.566$.

All options (A, B, C, D, E) are less than $4\pi$.

Question 10 (Is the number between 4 and 5? Select Yes/No)

A number $x$ is between 4 and 5 if $4

• Option A: $\boldsymbol{3\sqrt{2}}$

$3\sqrt{2}\approx4.242$, $x^2=(3\sqrt{2})^2 = 18$. $16<18<25$, so Yes.

• Option B: $\boldsymbol{2\sqrt{9}}$

$2\sqrt{9}=2\times3 = 6$. $6>5$, so No.

• Option C: $\boldsymbol{\frac{1}{3}\sqrt{80}}$

$\frac{1}{3}\sqrt{80}\approx\frac{1}{3}\times8.944\approx2.981<4$, so No.

• Option D: $\boldsymbol{\sqrt{17}}$

$\sqrt{17}\approx4.123$, $x^2 = 17$. $16<17<25$, so Yes.

• Option E: $\boldsymbol{2\sqrt{7}}$

$2\sqrt{7}\approx5.291>5$, so No.

Question 11 (Which square roots are irrational? Circle all that apply)

A square root is irrational if the number inside is not a perfect square. Perfect squares: $1^2 = 1, 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25, 6^2 = 36, 7^2 = 49$, etc.

• Option A: $\boldsymbol{\sqrt{10}}$

10 is not a perfect square, so $\sqrt{10}$ is irrational.

• Option B: $\boldsymbol{\sqrt{12}}$

12 is not a perfect square, so $\sqrt{12}$ is irrational.

• Option C: $\boldsymbol{\sqrt{16}}$

$\sqrt{16}=4$ (rational), so not irrational.

• Option D: $\boldsymbol{\sqrt{36}}$

$\sqrt{36}=6$ (rational), so not irrational.

• Option E: $\boldsymbol{\sqrt{49}}$

$\sqrt{49}=7$ (rational), so not irrational.

• Option F: $\boldsymbol{\sqrt{24}}$

24 is not a perfect square, so $\sqrt{24}$ is irrational.

Final Answers (Question-wise)

Question 8:

A. False
B. True
C. True
D. True
E. False

Question 9:

A, B, C, D, E

Question 10:

A. Yes
B. No
C. No
D. Yes
E. No

Question 11:

A, B, F