Art of Problem Solving

Square root property: Difference between revisions

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Created page with "The '''square root property''' is a method for solving quadratic equations. ==Method== First we must convert the quadratic to either t..."
 
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===First format===
===First format===


<math>x^2=18</math> take the square root of both sides
<math>x^2=18</math>  
 
take the square root of both sides
 
<math>x=\pm\sqrt{18}</math>
<math>x=\pm\sqrt{18}</math>



Revision as of 10:43, 15 May 2014

The square root property is a method for solving quadratic equations.

Method

First we must convert the quadratic to either the form $ax^2=b$ or $(yx+z)^2=w$.

First format

$x^2=18$

take the square root of both sides

$x=\pm\sqrt{18}$

so the roots are $\sqrt{18}$ and $-\sqrt{18}$.

Second format

$(3x+4)^2=5$ take the square root of both sides $3x+4=\pm\sqrt{5}$ isolate $x$ $x=\frac{\pm\sqrt{5}-4}{3}$

and those are the roots.