Is this theory regarding the graph and the square root valid?

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SUMMARY

The discussion centers on a method for calculating the square root of a number using a quadratic equation, specifically the formula $x^2 - 2x - 3$. Participants explore substituting $\sqrt{3}$ and $\sqrt{7}$ into the equation to find their respective square roots. The validity of this approach is questioned, particularly regarding the consistency of the results when substituting values. The conversation highlights the importance of careful manipulation of algebraic expressions in mathematical experimentation.

PREREQUISITES
  • Understanding of quadratic equations, specifically the form $ax^2 + bx + c$.
  • Familiarity with the concept of square roots and their properties.
  • Basic algebraic manipulation skills, including substitution and simplification.
  • Graphing techniques for visualizing quadratic functions and their intersections with the x-axis.
NEXT STEPS
  • Study the properties of quadratic equations and their graphs in detail.
  • Learn about the method of completing the square for solving quadratic equations.
  • Explore the implications of substituting values into algebraic expressions and the importance of consistency.
  • Investigate numerical methods for approximating square roots, such as the Newton-Raphson method.
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Mathematics students, educators, and anyone interested in algebraic methods for calculating square roots and understanding quadratic functions.

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http://mathhelpboards.com/pre-algebra-algebra-2/find-value-squareroot-3-using-graph-drawing-suitable-straight-line-19973.html

greg1313 said:
Mathematics is a science and experimentation is a valuable tool. The first thing I did was to substitute $\sqrt3$ for $x$ in the given quadratic and observe the results. Get your hands dirty!
I guess I found a method to obtain the square root of any number using the above graph.

$x^2-2x-3$ What I did to find the square root of 3 was replace $x^2$ with the desired square root

$\sqrt{3}^2-2x-3=3-2x-3=-2x=0=y$

And check this out if we replace the $x^2$ of the formula of the formula to obtain a square root of any number

$\sqrt{7}^2-2x-3=7-2x-3=-2x+4=0=y$

Check the $x$ axis of the intersection point of the graph and the x axis

Is this theory regarding the graph and the square root really valid?

[graph]z0awzx3ity[/graph]
 
Last edited:
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Re: An amazing discovery regarding the graph and the square root

mathlearn said:
$\sqrt{3}^2-2x-3=3-2x-3=-2x=0=y$
If [math]x = \sqrt{3}[/math] then [math]x^2 - 2x - 3 = (\sqrt{3})^2 - 2 \sqrt{3} - 3[/math]. You have to replace all the x's.

Also: [math]\sqrt{3}^2-2x-3=3-2x-3=-2x=0[/math] says that -2x = 0, but you originally had [math]x = \sqrt{3}[/math], which both can't be true.

-Dan
 

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