An exponent tells us the amount of times a number is to be multiplied by itself.
An exponent tells us the amount of times a number is to be multiplied by itself.
A root is the inverse operation of exponentiation, which helps us discover which number multiplied by itself gives this result.
The square root is equal to the power of 0.5.
\( 11^2= \)
\( 6^2= \)
\( \sqrt{64}= \)
\( \sqrt{36}= \)
\( \sqrt{49}= \)
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: We begin with the calculation .
Step 2: Perform the multiplication:
Let's examine a more structured multiplication method:
Multiply by (last digit of the second 11), we get 11.
Multiply by (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 . Upon reviewing the provided choices, the correct answer is choice 4: .
Therefore, the solution to the problem is .
121
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: The expression indicates we need to multiply 6 by itself.
Step 2: Calculating gives us 36.
Therefore, the value of is 36.
36
To solve this problem, we'll follow these steps:
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: , , , , , , , .
Step 3: We see that . Therefore, the square root of 64 is 8.
Therefore, the solution to this problem is .
8
Let's solve the problem step by step:
The square root of a number is a value that, when multiplied by itself, equals . This is written as .
We are looking for a number such that . This translates to finding .
We know that . Therefore, the principal square root of is .
Thus, the solution to the problem is .
Among the given choices, the correct one is: Choice 1: .
6
To solve this problem, we follow these steps:
Therefore, the solution to the problem is .
7
Which of the following is equivalent to the expression below?
\( \)\( 10,000^1 \)
Choose the expression that is equal to the following:
\( 2^7 \)
Choose the largest value
Sovle:
\( 3^2+3^3 \)
\( \sqrt{121}= \)
Which of the following is equivalent to the expression below?
To solve this problem, we will apply the rule of exponents:
Given the choices:
Therefore, the correct choice is , which simplifies to 10,000, making it equivalent to .
Thus, the expression is equivalent to:
Choose the expression that is equal to the following:
To solve this problem, we'll focus on expressing the power as a series of multiplications.
By comparing this expanded form with the provided choices, we see that the correct expression is:
Therefore, the solution to the problem is the expression that matches this expanded multiplication form, which is the choice .
Choose the largest value
Let's begin by calculating the numerical value of each of the roots in the given options:
We can determine that:
5>4>3>1 Therefore, the correct answer is option A
Sovle:
Remember that according to the order of operations, exponents precede multiplication and division, which precede addition and subtraction (and parentheses always precede everything).
So first calculate the values of the terms in the power and then subtract between the results:
Therefore, the correct answer is option B.
36
To solve the problem of finding the square root of 121, let's follow these steps:
Thus, the solution to the problem is .
11
\( \sqrt{100}= \)
\( \sqrt{144}= \)
\( \sqrt{x}=1 \)
\( X=? \)
\( \sqrt{36}= \)
\( \sqrt{x}=2 \)
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 , then should be our answer.
Step 1: Recognize that 100 is a perfect square. This means there exists an integer such that . Generally, we recall basic squares such as:
Step 2: Checking integers, we find that:
Step 3: Confirm the result: Since , then .
Step 4: Compare with answer choices. Given that one of the choices is 10, and , choice 1 is correct.
Therefore, the square root of 100 is 10.
10
To solve this problem, we proceed with the following steps:
Now, let's solve the problem:
Step 1: We need the square root .
Step 2: Recall that . We need to find .
Step 3: Recognize that 144 is a perfect square and find such that . Through either calculation or prior knowledge, we know:
.
Therefore, the square root of 144 is .
Thus, the solution to the problem is .
12
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: We have the equation .
Square both sides:
Step 2: Simplify both sides of the equation.
The left side simplifies to , since the square and the square root cancel each other out:
The right side simplifies to 1, so we have:
Therefore, the solution to the problem is .
1
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: A square root of a number is a value that, when multiplied by itself, gives the original number. Here, we want such that .
Step 2: We test integer values to find which one squared equals 36. Testing and gives:
-
-
-
-
-
-
Step 3: The integer satisfies . Therefore, .
Step 4: The correct choice from the given answer choices is 6 (Choice 4).
Hence, the square root of 36 is .
6
To solve the problem, follow these steps:
Now, let's proceed through each step:
Step 1: The given equation is .
Step 2: Square both sides: .
Step 3: This simplifies to .
Therefore, the value of that satisfies is .
Matching this solution with the provided choices, the correct answer is choice 3, which is 4.
4