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 TOPICS This page:   square roots    Search   Dr. Math See also the Dr. Math FAQ:   square/cube roots Internet Library:   exponents/roots MIDDLE SCHOOL About Math Algebra    equations    factoring expressions    graphing equations Arithmetic    division    exponents    factorials    factoring numbers    fractions/percents    logarithms Definitions Geometry    2-dimensional      conic sections/        circles      triangles/polygons    3D and higher      polyhedra History/Biography Logic Measurement    calendars/      dates/time    temperature    terms/units Number Sense    factoring numbers    negative numbers    pi    prime numbers    square roots Probability Puzzles Ratio/Proportion Statistics Word Problems Browse Middle School Square Roots Stars indicate particularly interesting answers or good places to begin browsing. Selected answers to common questions:     Square roots without a calculator.     Table of squares & square roots, 1-100. Surd Trick [02/14/2012] A student struggles to evaluate an expression with nested square roots. Doctor Vogler shares a substitution that starts with introducing more exponentiation. Table of Square Roots [05/12/2000] Do you have a table of square roots that are already worked out? To Identify Perfect Roots, Multiply, Guess, Memorize, or Factorize [06/21/2011] An adult learner wonders how to figure out perfect cube and square roots. Doctor Peterson outlines how to use factoring and informed guessing -- based on memorizing a few common powers -- and offers calculator guidance. Using Conjugates to Simplify Radicals [08/04/1998] When using conjugates, how do we know when to change the sign? For example, how would we simplify 1/[3+sqrt(3)-sqrt(6)]? Using the Ones Digit to Estimate Square Roots [02/11/2005] I am having trouble figuring out square roots quickly. For bigger numbers like 289, I have to try a lot of numbers before I get the answer. Is there some way to do this more easily? What is the Square Root of 8? [6/13/1996] What is the square root of 8? What's the Square Root of 75? [08/18/2002] Is the square root of 75 15(sqrt 5) or 5(sqrt 15)? Why Can't the Square Root of a Negative Number Be a Real Number? [12/07/2003] Can you explain why you can't find the square root of a negative number on the real number line? Why Does the Order of Square/Square Root Matter? [8/28/1996] Why does the square root of x^2 equal absolute value of x, but the square of the square root of x equals just plain old x? Why Do We Rationalize Fractions? [11/29/2005] Why do we have to simplify fractions that have a radical in the denominator to remove that radical and rationalize the denominator? Why is that important? Page: [

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