See also the
Dr. Math FAQ:
3D and higher
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.
- 2 Divided by the Square Root of 2 [11/10/1995]
Why does 2/sqrt 2 = sqrt 2 ?
- Adding Square Roots [12/26/2001]
What is the square root of 3 + the square root of 27?
- Finding Roots with a Scientific Calculator [05/15/2000]
How do you calculate the 8th root, or any other root, of a number using a
- Finding Square Roots [09/06/1998]
Can you explain why the algorithm for finding square roots works, without
- Finding square roots [6/17/1996]
How do you find the square root of a number?
- Formula for Calculating Square Roots [1/28/1995]
What is the formula for calculating square roots?
- Longhand Square Roots [03/30/1998]
How do you find the square root of any number? Is there an easy formula?
- Opposite of an Exponent [05/18/1997]
What is the opposite of an exponent?
- Square root of -1 [11/8/1994]
Hey Dr. Math - Do you know the square root of -1?
- Square Root of 3 [5/31/1996]
What is the square root of 3?
- Square Root of 64 [6/20/1996]
I would like to know the square root of 64.
- Square Roots and Exponents [2/2/1996]
What is a "square root" of something? What are "powers to 7"?
- Square Roots: Estimate, Divide, Average [02/04/1997]
Is there a longhand-division-and-guess method for finding square roots?
- Square Roots: Guess, Divide, Average [6/23/1996]
Is there a formula for finding square roots?
- 12 a Square Number? [11/07/2002]
Is 12 a square number? If it is, what is the square root of 12?
- 9x^2 = 64 [03/22/2003]
I am trying to figure out what 9x^2 = 64 is.
- Adding Radicals [9/11/1996]
How do I add radicals that aren't roots of perfect squares?
- Algebra for Equivalence [11/12/2011]
A teacher's warning about algebraic manipulations troubles a student. With simple
examples, Doctor Peterson shows how dividing by a variable may destroy solutions, how taking roots may introduce extraneous ones, and how factoring makes both more explicit, all while emphasizing caution with assumptions.
- Bakhshali Formula [12/15/2002]
I came across this formula for calculating square roots by hand.
- Calculating 4th Roots, 5th Roots... [05/05/1999]
Is there an easy way to calculate roots of any given depth?
- Calculators and Irrational Numbers [05/02/2001]
When I square the square root of 11 on any calculator, I get the answer
11 (exactly). That seems to indicate that the square root of 11 is a
rational number, but it's not. Can you explain this?
- Computing Square Roots Manually [03/05/1998]
Using the bisection method to compute square roots manually.
- Conventions of Square Roots [11/24/1998]
I think that the square root of 81 equals positive or negative 9, but my
teacher says that it is just positive 9...
- Decimal Square Roots [10/19/1998]
Is there any way to get a terminating decimal answer to a square root
without taking the square root of a perfect square?
- Definition of Negative Square Roots [03/08/2004]
I know that the square root of 49 = 7 since 7 x 7 = 49. But the
negative square root of 49 is -7. Is this because (-7) x (-7) also
equals 49 or because the square root of 49 is 7 and the negative stays
because it is not involved with the operation? My teacher wrote
-SQRT(49) = -7 because (-7) x (-7) = 49.
- Dividing and Multiplying Radicals [03/07/1999]
How do you multiply the square root of 3/4 by the square root of 4/5?
- Dividing Radicals [02/15/1999]
How do you simplify 7 sqrt32 / (5 sqrt63) ?
- Edge of a Cube Given Volume [10/06/1997]
I am a teacher currently teaching volume to a class of Grade 5 pupils.
- Exact Answers for Square Roots [04/16/2006]
My teacher says that one of the problems with using calculators is
that you don't always get exact answers. I don't understand why.
Aren't calculators accurate?
- Finding a Square Root by Reasoning [11/18/2004]
What's the square root of 40,000,000? I can't figure it out.
- Finding Square Roots [02/07/2002]
I would like to know what the square root of 3612 is.
- Fractional Exponents [12/07/2003]
When a number is raised to a power like 4/3 or 3/5, how is it done?
- How Can the Product of Two Radicals Be Finite? [06/27/2006]
How is it possible that sqrt(5) * sqrt(20), each of which is by itself
an infinite number, can make exactly 10 when they are multiplied?
- How to Pronounce a Fraction of a Percentage [07/07/2005]
Is it correct to say "one tenth of one percent" as opposed to saying "one tenth percent" for 0.1%? Why or why not?
- Irrational Equations [06/02/2002]
I know what a rational equation is, but what's an irrational equation?
- Is 14798678562 or 15763530163289 a Perfect Square? [12/08/2002]
Examine both the units digits and the digital roots of perfect squares
to help determine whether or not a given number is a perfect square.
- Line Segment Representing Sqrt(3) [10/07/2002]
Draw a line segment that represents radical 3.
- Manual Method for Finding Square Roots [9/11/1995]
I'm looking for a manual method to find a square root of a number. Many
years ago we were taught how to do it, but my memory is failing me, and
with the calculator it's too easy.
- Mental Math Tricks - Finding Two Digit Square Roots [12/03/2003]
Do you know if there is any trick behind looking at a number which is
the result of a two digit number having been squared and being able to
tell what the number was that was squared?
- Method to Find Square Root of Pi [03/30/1997]
How do I calculate the square root of Pi?