# SOLUTION: please show the conjecture is false by coming up with a counterexample. the square root of a number x is always less than x.

Algebra ->  Algebra  -> Equations -> SOLUTION: please show the conjecture is false by coming up with a counterexample. the square root of a number x is always less than x.      Log On

 Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

 Algebra: Equations Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Equations Question 206509: please show the conjecture is false by coming up with a counterexample. the square root of a number x is always less than x.Found 2 solutions by jim_thompson5910, stanbon:Answer by jim_thompson5910(28476)   (Show Source): You can put this solution on YOUR website! Start with the given inequality. To prove this false with a counter-example, we need to use a small number (that is less than 1). I'm going to use (since ) Plug in Break up the root. Evaluate the square root of 1 to get 1. Evaluate the square root of 4 to get 2. Cross multiply (this will help us determine which side is larger) Multiply Since the inequality is FALSE, this means that is FALSE (it turns out that one-half is actually larger than a quarter...draw out a picture to verify yourself). So this means that is also false. So we've shown that the inequality is false for all real numbers. Note: it turns out that is only true if Answer by stanbon(57214)   (Show Source): You can put this solution on YOUR website!sqrt(1/4) = 1/2 and 1/2 is greater than 1/4 ================================ Cheers, Stan H.