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<html><table height="500" width="1000" border="2"><TR height="5" width="1000"><strong><center><marquee><font color="Green"><h1>APTITUDE</h1></center></strong></font></TR></marquee><TR><TD align="left" width="200" valign="top"><table><TR><a href="numbers.html"><strong>Numbers</strong></a></TR><br><TR><a href="hcf.html"><strong>H.C.F and L.C.M</strong></a></TR><br><TR><a href="dec.html" ><strong>Decimal Fractions</strong></a></TR><br><TR><a href="simplification.html"><strong>Simplification</strong></a></TR><br><TR><a href="squareandcuberoot.html" ><strong>Square and Cube roots</strong></a></TR><br><TR><a href="average.html" ><strong>Average</strong></a></TR><br><TR><a href="pnumbers.html" ><strong>Problems on Numbers</strong></a></TR><br><TR><a href="problemsonages.html"><strong>Problems on Ages</strong></a></TR><br><TR><a href="surdsandindices.html"><strong>Surds and Indices</strong></a></TR><br><TR><a href="percent.html" ><strong>Percentage</strong></a></TR><br><TR><a href="profitandloss.html" ><strong>Profit and Loss</strong></a></TR><br><TR><a href="ratioandproportion.html" ><strong>Ratio And Proportions</strong></a></TR><br><TR><a href="partnership.html"><strong>Partnership</strong></a></TR><br><TR><a href="chainrule1.html"><strong>Chain Rule</strong></a></TR><br><TR><a href="timeandwork.html" ><strong>Time and Work</strong></a></TR><br><TR><a href="pipesandcisterns.html" ><strong>Pipes and Cisterns</strong></a></TR><br><TR><a href="timeanddistance.html"><strong>Time and Distance</strong></a></TR><br><TR><a href="trains.html" ><strong>Trains</strong></a></TR><br><TR><a href="boats.html"><strong>Boats and Streams</strong></a></TR><br><TR><a href="alligation.html"><strong>Alligation or Mixture </strong></a></TR><br><TR><a href="simple.html" ><strong>Simple Interest</strong></a></TR><br><TR><a href="CI.html"><strong>Compound Interest</strong></a></TR><br><TR><a href=""><strong>Logorithms</strong></a></TR><br><TR><a href="areas.html" ><strong>Areas</strong></a></TR><br><TR><a href="volume.html"><strong>Volume and Surface area</strong></a></TR><br><TR><a href="races.html" ><strong>Races and Games of Skill</strong></a></TR><br><TR><a href="calendar.html" ><strong>Calendar</strong></a></TR><br><TR><a href="clocks.html" ><strong>Clocks</strong></a></TR><br><TR><a href="" ><strong>Stocks ans Shares</strong></a></TR><br><TR><a href="true.html" ><strong>True Discount</strong></a></TR><br><TR><a href="banker1.html" ><strong>Bankers Discount</strong></a></TR><br><TR><a href="oddseries.html"><strong>Oddmanout and Series</strong></a></TR><br><TR><a href=""><strong>Data Interpretation</strong></a></TR><br><TR><a href="probability.html"><strong>probability</strong></a></TR><br><TR><a href="percom1.html"  ><strong>Permutations and Combinations</strong></a></TR><br><TR><a href="pinkivijji_puzzles.html" ><strong>Puzzles</strong></a></TR></table></TD><head><center><b>SQUARE ROOTS AND CUBE ROOTS</b></center></head><body><pre> Formula:<br>    The Product of two same numbers in easiest way as follow.<br><br>Example: let us calculate the product of 96*96<br>Solution:  Here every number must be compare with the 100.<br>           See here the given number 96 which is 4 difference with the 100.<br>                         so subtract 4 from the 96 we get 92 ,<br>                        then the square of the number 4 it is 16.<br>                      place the 16 beside the 92<br>                                we get answer as 9216.<br>          9 6<br>       -    4<br>    --------------<br>         9  2<br>  --------------<br>         4*4=16<br>                       9 2 1 6 <br>  therefore square of the two numbers 96*96=9216.<br><br>Example: Calculate  product for  98*98<br>Solution: Here the number 98 is having 2 difference when compare to 100<br>         subtract 2 from the number then we get 96<br>             square the number 2 it is 4<br>                 now place beside the 96<br>                   as 9604<br>        9 8       -   2  -------------       9 6 -------------     2*2=4                            9 6 0 4.                   so, we get the product of 98*98=9604. Example : Calculate product for 88*88   Solution:  Here the number 88 is having 12 difference when compare to 100<br>                 subtract 12 from the 88 then we get 76 <br>the square of the number 12 is 144          (which is three digit number but should place only two digit beside the 76)<br>            therefore in such case add one to 6 then it becomes 77 <br>                 now place 44 beside the number 77<br>                      we will get 7744 .<br>               answer will be 7744.<br>            88          -12      ------------           76       -----------                     12*12=144             76          +   144    --------------------            7744   --------------------      Example: Find the product of the numbers  46 *46?<br>  Solution:                   consider the number 50=100/2<br>          now again go comparision with the number which gets when division with 100.<br>here consider the number 50 which is nearer to the number given.<br>         46 when compared with the number 50 we get the difference of 4.<br>           now subtract the number 4 from the 46,     we get 42.<br>              as 50 got when 100 get divided by 2.<br>                so, divided the number by 2 after subtraction.<br>                           42/2=21<br>          now square the the number 4 i.e, 4*4=16<br>     just place the number 16 beside the number 21<br>              we get 2116.<br>                 4 6                   4        ----------------                4 2                         as     50  =  100/2                42/2=21        now place 4*4=16 beside 21                            2 1 1 6        Answer will be  2116.Example: Find the product of the numbers 37*37<br>Solution:                                consider the number 50=100/2          now again go comparision with the number which gets when division with 100.here consider the number 50 which is nearer to the number given.    37 when compared with the number 50 we get the difference of 13.           now subtract the number 13 from the 37,     we get 24.              as 50 got when 100 get divided by 2.                so, divided the number by 2 after subtraction.                           24/2=12          now square the the number 13 i.e, 13*13=169     just place the number 169 beside the number 21    now as 169 is three digit number then add 1 to 2 we get 1t as 13 then place 69 beside the 13              we get 1369.      3 7      1 3 -----------------      2 4                               as    50  =  100/2    24/2=12             square 13* 13=169                1 2           +     1 6 9    -----------------------              1 3  6  9  -------------------------Example: Find the product of 106*106<br>  Solution: now compare it with 100 ,    The given number is more then 100    then add the extra  number to the given number.           That is 106+6=112   then square the number 6     that is 6*6=36    just place beside the number 36 beside the 112,then             we get 11236.             1 0 6       +         6  ---------------------            1 1 2--------------------                   now 6* 6=36 place this beside the number 112, we get       1 1 2 3 6<br><br>  Square root: If x2=y ,we say that the square root of y is x and we write ,y<sup>1/2</sup>=x.  Cube root : The cube root of a given number x is the number whose cube is x. we denote the cube root of x by x1/3 .<br>Examples:   1.Evaluate 鈭
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