Question

Jenny multiplies the square root of her favorite positive integer by $\sqrt{2}$. Her product is an integer. a) Name three numbers that could be Jenny's favorite positive integer, and explain why each could possibly be Jenny's favorite integer. b) Suppose Jenny divides the square root of her favorite positive integer by sqrt(2). Does she have to get an integer? (Remember, when Jenny multiplies the square root of her favorite integer by sqrt(2), she gets an integer.)

Answer 1

Answer:

Part a) $2,50,18$

Part b) When Jenny divides the square root of her favorite positive integer by $\sqrt{2}$, she gets an integer

Step-by-step explanation:

Let

x-------> the favorite positive integer

Part a)

1) For $x=2$

$\sqrt{2}*\sqrt{2}=\sqrt{4}=2$ -----> the product is an integer

so

The number $x=2$ could be Jenny favorite positive integer

2) For $x=50$

$\sqrt{50}*\sqrt{2}=\sqrt{100}=10$ -----> the product is an integer

so

The number $x=50$ could be Jenny favorite positive integer

3) For $x=18$

$\sqrt{18}*\sqrt{2}=\sqrt{36}=6$ -----> the product is an integer

so

The number $x=18$ could be Jenny favorite positive integer

Part B)

1) For $x=2$

$\sqrt{2}/\sqrt{2}=\sqrt{1}=1$ -----> the result is an integer

2) For $x=50$

$\sqrt{50}/\sqrt{2}=\sqrt{25}=5$ -----> the result is an integer

3) For $x=18$

$\sqrt{18}/\sqrt{2}=\sqrt{9}=3$ -----> the result is an integer

Therefore

When Jenny divides the square root of her favorite positive integer by $\sqrt{2}$ , she gets an integer