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.
\( \sqrt{100}= \)
Everything you need to know about the root of negative numbers is that... it simply does not exist!
Negative numbers do not have a root, if in an exam you come across an exercise involving the root of a negative number, your answer should be that it has no solution.
Want to understand the logic? Keep reading.
The root is some number, let's suppose one that we will call that, in fact, will be positive and that, when multiplied by itself will give us .
For example, the root of will be a positive number that if we multiply it by itself we will obtain .
That is, .
Instead of saying "multiply it by itself" we can say "raise it to the square".
\( \sqrt{16}= \)
\( \sqrt{25}= \)
\( \sqrt{36}= \)
As we have seen, the root of any number, for example, is a positive number that if we square it will give us .
There is no positive number in the whole world that when squared will give us a negative number, therefore, negative numbers do not have a root.
Solve the exercise:
If we raise to the power of two, we will get .
Another exercise
We will not be able to find any positive number that, when squared, gives us since any positive number squared will be positive and never negative.
\( \sqrt{36}= \)
\( \sqrt{49}= \)
\( \sqrt{4}= \)
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 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 need to determine the square root of 25.
Therefore, the solution to the problem is .
The correct answer is choice 2: 5.
5
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
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