Powers and Roots Practice Problems - Basic Exponents

To solve this problem, we'll follow these steps:

• Step 1: Set up the multiplication as $11 \times 11$.
• Step 2: Compute the product using basic arithmetic.
• Step 3: Compare the result with the provided multiple-choice answers to identify the correct one.

Now, let's work through each step:
Step 1: We begin with the calculation $11 \times 11$.
Step 2: Perform the multiplication:

1. Multiply the units digits: $1 \times 1 = 1$.
2. Next, for the tens digits: $11 \times 10 = 110$.
3. Add the results: $110 + 1 = 111$. This doesn't seem right, so let's break it down further.

Let's examine a more structured multiplication method:

Multiply $11$ by $1$ (last digit of the second 11), we get 11.
Multiply $11$ by $10$ (tens place of the second 11), we get 110.

If we align correctly and add the partial products:

     11
+   110
------------
   121

Step 3: The correct multiplication yields the final result as $121$. Upon reviewing the provided choices, the correct answer is choice 4: $121$.

Therefore, the solution to the problem is $121$.

To solve this problem, we'll follow these steps:

• Step 1: Recognize that $6^2$ means $6 \times 6$.
• Step 2: Perform the multiplication of 6 by itself.

Now, let's work through each step:
Step 1: The expression $6^2$ indicates we need to multiply 6 by itself.
Step 2: Calculating $6 \times 6$ gives us 36.

Therefore, the value of $6^2$ is 36.

The task is to find the square root of the number 100. The square root operation seeks a number which, when squared, equals the original number. For any positive integer, if $x^2 = 100$, then $x$ should be our answer.

Step 1: Recognize that 100 is a perfect square. This means there exists an integer $x$ such that $x \times x = 100$. Generally, we recall basic squares such as:

• $1^2 = 1$
• $2^2 = 4$
• $3^2 = 9$
• and so forth, up to $10^2$

Step 2: Checking integers, we find that:

$10^2 = 10 \times 10 = 100$

Step 3: Confirm the result: Since $10 \times 10 = 100$, then $\sqrt{100} = 10$.

Step 4: Compare with answer choices. Given that one of the choices is 10, and $\sqrt{100} = 10$, choice 1 is correct.

Therefore, the square root of 100 is 10.

To solve this problem, we'll follow these steps:

• Step 1: Recognize what finding a square root means
• Step 2: List known perfect squares to identify which one results in 64
• Step 3: Verify the square root by calculation

Now, let's work through each step:
Step 1: To find the square root of 64, we seek a number that, when multiplied by itself, equals 64.
Step 2: Consider the sequence of perfect squares: $1^2 = 1$, $2^2 = 4$, $3^2 = 9$, $4^2 = 16$, $5^2 = 25$, $6^2 = 36$, $7^2 = 49$, $8^2 = 64$.
Step 3: We see that $8^2 = 64$. Therefore, the square root of 64 is 8.

Therefore, the solution to this problem is $8$.

To solve this problem, we want to find the square root of 9.

Step 1: Recognize that a square root is a number which, when multiplied by itself, equals the original number. Thus, we are seeking a number $x$ such that $x^2 = 9$.

Step 2: Note that 9 is a common perfect square: $9 = 3 \times 3$. Therefore, the square root of 9 is the number that, when multiplied by itself, gives 9. This number is 3.

Step 3: Since we are interested in the principal square root, we consider only the non-negative value. Hence, the principal square root of 9 is 3.

Therefore, the solution to the problem is $3$.