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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.

Subtleties of Radical Equations [12/07/2003]
Can you explain how to solve radical equations, like sqrt(5x) = 1.5?

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?

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