There is no root of a negative number since any positive number raised to the second power will result in a positive number.
There is no root of a negative number since any positive number raised to the second power will result in a positive number.
Choose the largest value
\( \sqrt{64}= \)
\( \sqrt{36}= \)
\( \sqrt{49}= \)
Solve the following exercise:
\( \sqrt{x^2}= \)
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
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
Solve the following exercise:
In order to simplify the given expression, we will use two laws of exponents:
a. The definition of root as an exponent:
b. The law of exponents for power of a power:
Let's start with converting the square root to an exponent using the law mentioned in a':
We'll continue using the law of exponents mentioned in b' and perform the exponent operation on the term in parentheses:
Therefore, the correct answer is answer a'.
\( 5+\sqrt{36}-1= \)
\( \sqrt{441}= \)
\( \sqrt{225}= \)
\( \sqrt{144}= \)
\( \sqrt{121}= \)
To solve the expression , we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Here are the steps:
First, calculate the square root:
Substitute the square root back into the expression:
Next, perform the addition and subtraction from left to right:
Add 5 and 6:
Then subtract 1:
Finally, you obtain the solution:
The root of 441 is 21.
To solve the problem, we will follow these steps:
Now, let's work through the steps:
Step 1: The perfect squares around 225 are , , and .
Step 2: We calculate , therefore, .
Therefore, the solution to the problem is .
Accordingly, the correct answer choice is option 2: 15.
15
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 the problem of finding the square root of 121, let's follow these steps:
Thus, the solution to the problem is .
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\( \sqrt{100}= \)
\( \sqrt{64}= \)
\( \sqrt{36}= \)
\( \sqrt{16}= \)
\( \sqrt{9}= \)
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'll determine the square root of 64, following these steps:
Now, let's work through each step:
Step 1: We are tasked with finding . The problem involves identifying the number which, when squared, results in 64.
Step 2: To find this number, we'll check our knowledge of squares. We know that 8 is a significant integer whose square results in 64.
Step 3: Compute: . Hence, meets the requirement.
We find that the solution to the problem is .
8
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:
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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 determine the square root of 16, follow these steps:
Hence, the solution to the problem is the principal square root, which is .
4
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 such that .
Step 2: Note that 9 is a common perfect square: . 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 .
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