You are here:

Algebra/Square Roots


How do I find the long-hand way to figure out square and cubed roots? I mean I know cube root of 27 is 3 off the top of my head, and square root of 81 is 9, but I have no idea how that is figured out other than memorizing it from somewhere.

If we want the square root of, say, 2314, we divide it into 2-digit sections.
This gives 23 14.  The square that is less than 23 is 4, for 4^2 = 16.
Subtracting that off gives 23 - 16 = 7, so next look at 714.

Take 2*(what we have so far), which is 4, and get 8.
Find x where eighty-x times x is less than 714.
It can be seen that 88*8 = 704, so the next digit is 8.
This makes 48 the number right now, and 48^2 = 2,304.

To find the next digit, take the difference, which is 714 - 704 = 10.
Add two more zeros to that and get 1000.
The number we have so far is 48, and 2*48 = 96.
Find nine hundred and sixty x times x, and we can see that x = 1.
Subtract of 961x1 = 961 and get 39.  Add two more zeros to get 3900 and repeat the process.

Thus, so far, we have 48.1.
Looking at 48.1^2, it is 2314.61, which is still less than 2314.

The next step would be taking 962x times x where the result is less than 3900.
It looks like this one is a 0, for nine thousand six hundred and twenty one times one
is too large.  So far, we now have 48.10.

As far as cube roots, I never did remember how to do them, but did read it can be done.  It took a several page explanation in how to do them.


All Answers

Answers by Expert:

Ask Experts


Scott A Wilson


Any algebraic question you've got. That includes question that are linear, quadratic, exponential, etc.


I have solved story problems, linear equations, parabolic equations. I have also solved some 3rd order equations and equations with multiple variables.

Documents at Boeing in assistance on the manufacturiing floor.

MS at math OSU in mathematics at OSU, 1986. BS at OSU in mathematical sciences (math, statistics, computer science), 1984.

Awards and Honors
Both my BS and MS degrees were given with honors.

Past/Present Clients
Students in a wide variety of areas since the 80's; over 1,000 of them have been in algebra.

©2017 All rights reserved.