Question

which one doesnt belong? give at least two explanations or examples for why one item does not belong in the group. a: $sqrt{30}$, b: $sqrt{27}$, c: $sqrt{128}$, d: $sqrt{36}$. head problem. solve the following using no paper, pencil or calculator. think of the number of legs on a cow, triple that number, cut that number in half, square that number, find the sum of the digits, what is the square root of that number

Explanation:

Step1: Analyze "Which One Doesn't Belong?"

• $\sqrt{30}$ is an irrational number. $\sqrt{27}=3\sqrt{3}$ is irrational. $\sqrt{36} = 6$ is rational. $\sqrt{128}=8\sqrt{2}$ is irrational. So $\sqrt{36}$ (D) is different as it is the only one with a rational - valued square - root. Another reason: $\sqrt{30}$, $\sqrt{27}$, and $\sqrt{128}$ cannot be simplified to a whole number, while $\sqrt{36}=6$ is a whole number.

Step2: Solve "Head Problem"

• A cow has 4 legs.
• Triple 4: $4\times3 = 12$.
• Cut in half: $\frac{12}{2}=6$.
• Square 6: $6^2 = 36$.
• Sum of digits of 36: $3 + 6=9$.
• Square - root of 9: $\sqrt{9}=3$.

Answer:

1. For "Which One Doesn't Belong?": $\sqrt{36}$ (D) doesn't belong because it is the only one with a rational square - root and the only one that simplifies to a whole number.
2. For "Head Problem": 3