- #1
lioric
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How is it equal to v in the end?
I'm sorry for asking such questions. But I'm just trying to understand
Square Root Simplified: Understanding the Result as a Single Nonnegative Number
- Thread starter lioric
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In summary, the conversation discusses simplifying expressions involving the square root of u^2 / c^2 and how it is equal to v in the end. The process involves canceling out terms and taking only the positive root in the final answer. However, there is a discrepancy between the solution shown in the original post and the one shown in another book.
How is it equal to v in the end?
I'm sorry for asking such questions. But I'm just trying to understand
- #2
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Because addition is associative and commutative and ##c^2≠0##. For short: just calculate the left hand side.
- #3
DrClaude
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Can you simplify the denominator?
- #4
lioric
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Dear god I must be blindDrClaude said:
v^2-v^2 = 0
c^2 and c^2 cancels
And all that's left is a rooted v^2 which cancels itself
But look at this
This is how the same solution is illustrated in another book.
(1-u^2/c^2) cancels each other
The u^2 subtracts each other in the denominator like in the previous sollution
Which leaves a rooted u^2 / c^2
How does that simplify?
- #5
DrClaude
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Look to the left of the square root sign...lioric said:
- #6
lioric
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I can see the c root What does it mean?DrClaude said:
- #7
DrClaude
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No, it's c times the root.lioric said:
- #8
lioric
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So are you saying that the large root will cancel the squares of u^2 / c^2 making it like u / c * c/1DrClaude said:
and c and c cancels?
- #9
DrClaude
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Yes. Note that the author there takes only the positive root, while in the OP the two roots are kept.lioric said:
- #10
lioric
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Thank you very muchDrClaude said:
- #11
Mark44
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This is actually incorrect. On the right side it should be |v|, not ##\pm v##. In other words, the square root evaluates to a single nonnegative number, not two numbers.lioric said:
Related to Square Root Simplified: Understanding the Result as a Single Nonnegative Number
What is a square root and why is it important?
A square root is a mathematical operation that finds the number which, when multiplied by itself, gives a certain number. It is important because it allows us to find the length of a side in a right triangle, to solve equations, and to simplify radical expressions.
How do I simplify a square root?
To simplify a square root, you can factor the number inside the radical and remove any perfect square factors. Then, write the remaining factors as the square root of a whole number. For example, the square root of 18 can be simplified to the square root of 9 times the square root of 2, which becomes 3√2.
Can all square roots be simplified?
No, not all square roots can be simplified. Some square roots, like √5 or √7, are irrational numbers and cannot be simplified to a whole number. They can only be written in decimal form or as an infinite series.
What is the difference between simplifying and rationalizing a square root?
Simplifying a square root involves simplifying the number inside the radical, while rationalizing a square root involves removing any radicals from the denominator of a fraction. Rationalizing is usually done to make expressions easier to work with or to eliminate imaginary numbers.
What are some real-world applications of simplifying square roots?
Simplifying square roots has many real-world applications, such as calculating the height of a tree or building, finding the length of a diagonal in a rectangle, or determining the amount of wire needed to fence a circular garden. It is also used in fields such as engineering, physics, and finance.
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