1. Copy and paste the following between your HEAD tags:-

sqrtT.innerHTML="";
sqrT.innerHTML="";
difT.innerHTML="";
sqrt.innerHTML="";
sqr.innerHTML="";
dif.innerHTML="";
line.innerHTML="";
var initsquare=parseInt(SRProgress.startSquare.value);
if (initsquare<1 || initsquare==""){alert("This number should be greater than zero!");SRProgress.startSquare.focus();return false}
var finalsquare=SRProgress.finalSquare.value;
if (initsquare>=finalsquare){alert("The second number should be greater than the first!");SRProgress.finalSquare.focus();SRProgress.finalSquare.select();return false}
var diff=finalsquare-initsquare;
var amtAdd=((initsquare*2)+diff)*diff;
initSquare.innerHTML="Initial Square ["+initsquare+"²"+"]";
initSquareR.innerHTML=Comma(Math.pow(initsquare,2));
dblInit.innerHTML="Next: double initial square root";
dblInitR.innerHTML="["+initsquare+"x2="+initsquare*2+"]";
addDiff.innerHTML="Next: add difference to above"; 
addDiffR.innerHTML="["+diff+"+"+initsquare*2+"="+parseInt((initsquare*2)+diff)+"]";

amountToAdd.innerHTML="Next: multiply this by difference ["+Comma(parseInt((initsquare*2)+diff))+"x"+diff+"]";
amountToAddR.innerHTML=Comma(((initsquare*2)+diff)*diff);
finalSquare.innerHTML="Final Square ["+finalsquare+"²"+"] = ["+Comma(initsquare)+"²"+"+"+Comma(((initsquare*2)+diff)*diff)+"]";
finalSquareR.innerHTML=Comma(Math.pow(finalsquare,2));

if (SRProgress.choice[0].checked==true)
{line.innerHTML="<hr>";
sqrtT.innerHTML="Square Root";
difT.innerHTML="Make-up";
sqrT.innerHTML="Square";

for (x=initsquare; x<=finalsquare; x++)
{sqrt.innerHTML=sqrt.innerHTML+x+"<br>";
dif.innerHTML=dif.innerHTML+Comma(Math.pow((x-1),2))+"+"+parseInt(((x-1)*2+1))+" =["+(x-1)+"²"+"+"+(x-1)+"x2+1]"+"<br>";
sqr.innerHTML=sqr.innerHTML+Comma(Math.pow(x,2))+"<br>"}
	}
}

function CheckAll(){
if (SRProgress.startSquare.value!="" && SRProgress.finalSquare.value!="")
{SRProgress.difference.value=SRProgress.finalSquare.value-SRProgress.startSquare.value}
}

function putFocus(formInst, elementInst)
{document.forms[0].elements[0].focus()}
</script>

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2. Copy and paste the following code between your BODY tags where you want the input displayed:
<div style="position:absolute; left:250; top:225">
<center><table width=100% border=0 bordercolor=#ffff00 cellspacing="0" cellpadding="10"><tr><td>

<center><h3>Square Root Progression</h3></center>
The methods outlined below are intended as aids to mental arithmetic in multiplication.
<p>The simple rule for progressing from one square root to another is as follows:-<ol>
<li>Double the <i>Starting Square Root. <span style="color:#ff0000">[Result 1]</span></i>.
<li>Add the difference between the <i>Starting</i> and <i>Ending</i> Square roots to Result 1 <span style="color:#ff0000">[Result 2]</span>.
<li>Multiply Result 2 by the difference. <span style="color:#ff0000">[Result 3]</span>
<li>Add Result 3 to the original square to get the final square root.</ol>
Example:-
To move from the square root of 9 to the square root of 15.<ol>
<li>Difference between 15 and 9 = 6.
<li>Double  starting square: 9+9 and add difference (6) giving us 24.
<li>Multiply 24 by difference 6 = 144.
<li>The square of 9 = 81 + 144 = 225 (square root of 15).</ol>
<p>Knowledge of square root progression could be important in determining the factors of some numbers.
<p>For instance, say you had a number like 391. On the face of it, it isn't obvious that 391 has prime factors. But we know that if you add 9 (a perfect square) to 391 we get 400 (a perfect square).
<p>Those facts tell us 391 must have prime factors. See <a href="datFactors_Of_Number.asp"><span onmouseover="this.className='Over'" onmouseout="this.className='OFF'"> Prime Factors Of A Number</span></a>. Given 20 is the square root of 400 and 3 is the square root of 9, the answer lies 20 ± 3 which gives 17 and 23 - the factors of 391.
<p>Input the appropriate figures below to explore other numbers.
<br><br>

<fieldset>
<legend id="legend" align="center" style="color:#ff0000;font-size:16">Square Root Progression</legend>
<table width=100% border=0 bordercolor=#0000ff cellspacing="0" cellpadding="2"><tr><td>
<form name="SRProgress" method="post">
Initial Square Root ==>==>
<td><input type="text" name="startSquare" onKeyPress="if ((event.keyCode<48) || (event.keyCode>57)) event.returnValue=false" onClick=value="" onBlur="CheckAll()" size=18>

<tr><td>
Final Square Root ==>==>
<td><input type="text" name="finalSquare" onKeyPress="if ((event.keyCode<48) || (event.keyCode>57)) event.returnValue=false" onClick=value="" onBlur="CheckAll()" size=18>

<tr><td>
Difference ==>==>==>==>
<td><input type="text" name="difference" disabled size=18>

<tr><td>
Do you want to see a progression list?
<td><label for="yes" style="color:#ff0000">Yes==></label>
<input type="radio" id="yes" name="choice" value="yes" checked onClick="Square_Root_Progression()">
<label for="no" style="color:#000000">No==></label>
<input type="radio" id="no" name="choice" value="no" onClick="Square_Root_Progression()">

<tr><td colspan=2 style="color:#0000ff" id="amountToAdd">
	<td colspan=2 style="color:#ff0000;text-align:right" id="amountToAddR">
<tr><td colspan=2 style="color:#0000ff" id="finalSquare">
	<td colspan=2 style="color:#0000ff;text-align:right" id="finalSquareR">
<tr><td colspan=6 id="line">
<tr><td id="sqrtT">
	<td id=difT>
	<td id="sqrT">
<tr><td id="sqrt">
	<td id="dif">
	<td id="sqr">	
</form>
</td></tr></table>
</fieldset>
</div>
                     *********************************
Please Note
You can display where ever you like. You change the "left" and "top" values in the opening "div" tag above to whatever values you need. 
a) "top" is the vertical distance of the top left corner of the display starting at zero. The higher the number the lower down the page.
b) "left" is the horizontal distance of the top left corner of the display starting at zero. The higher the number the further across the page.
c) You can change also the color of the display and the background.

If you have any problems or questions please email us at info@datedial.com.

Linking Information:-
TITLE : Square Root Progression
URL : http://www.datedial.com/datSquare_Root_Progression.asp
DESCRIPTION : How we progress from one square root to another.