Solving the Mystery of Square Root x Multiplied by 1/x

In summary, the mystery behind square root x multiplied by 1/x is that the result is always equal to 1, regardless of the value of x. This is because we are multiplying a number by its square root, which is typically a fraction. This concept is used in various real-life applications and can be proven mathematically using the laws of exponents. For example, when x=4, the result of square root 4 multiplied by 1/4 is 1. Understanding this mystery can be useful in simplifying expressions and solving equations, as well as understanding the relationship between inverse operations.
  • #1
Altami
17
0
How is squareroot(x)*(1/x)= 1/square root x

can somebody please explain this? I think I am having a brain lockup...
 
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  • #2
Let y=√x, the x=y². So √x/x = y/y² = 1/y = 1/√x.
 
  • #3
mathman said:
Let y=√x, the x=y². So √x/x = y/y² = 1/y = 1/√x.

Thank you! For some reason I couldn't think of the reason to make the statement true.

Life saver!
 

Related to Solving the Mystery of Square Root x Multiplied by 1/x

1. What is the mystery behind square root x multiplied by 1/x?

The mystery lies in the fact that when we multiply a number by its reciprocal, we get a result of 1. However, in this case, we are multiplying a number by its square root, which is typically a fraction. This leads to an unexpected solution.

2. What is the solution to this mystery?

The solution is that the result of square root x multiplied by 1/x is always equal to 1, regardless of the value of x. This can be proven mathematically using the laws of exponents.

3. How does this relate to real-life applications?

This mystery is a fundamental concept in mathematics and is used in various real-life applications, such as engineering, physics, and finance. It helps us understand the relationship between a number and its reciprocal.

4. Can you provide an example to illustrate this mystery?

For instance, if we take x=4, then the square root of 4 is 2. When we multiply 2 by its reciprocal, which is 1/2, we get a result of 1. This is true for any value of x.

5. How can understanding this mystery be useful in problem-solving?

Understanding this mystery can be helpful in simplifying mathematical expressions and solving equations. It also helps us grasp the concept of inverse operations and their relationship to each other.

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