Question

1. (175) is the following sentence true? you can undo a root by raising it to a power. a) yes b) no c) maybe d) sometimes e) not applicable 2. (178) is the following sentence true? the pythagorean theorem states that the sum of the legs of a right - triangle is equal to the hypotenuse. a) yes b) no c) maybe d) sometimes e) not applicable 3. (174) calculate the value of the expression: \\(\sqrt{9^{2}}\\) a) 3 b) 11 c) 19 d) 9 e) 27

Explanation:

Step1: Analyze first statement

If we have a square - root (a type of root) $\sqrt{x}$, raising it to the power of 2 (for square - root) gives back $x$. For example, if $x = 4$, $\sqrt{4}=2$ and $2^{2}=4$. In general, if $y = \sqrt[n]{x}$, then $y^{n}=x$. So, you can undo a root by raising it to a power.

Step2: Analyze second statement

The Pythagorean Theorem states that for a right - triangle with legs $a$ and $b$ and hypotenuse $c$, $a^{2}+b^{2}=c^{2}$, not $a + b=c$. So the statement is false.

Step3: Calculate the expression

First, $9^{2}=81$. Then $\sqrt{9^{2}}=\sqrt{81}=9$.

Answer:

1. a) Yes
2. b) No
3. d) 9