Square roots

From Math Wiki

1 Questions or Issues
2 Prime Factorization
- 2.1 Prime Factorization
- 2.2 EXAMPLE
3 Simplifying
4 Adding and simplifying square roots
5 Multiplying and Dividing Square Roots
6 External Links

Questions or Issues

If you still have questions or problems with square roots, whether it be simplifying, adding, multiplying, dividing, or anything else, just ask it right here and we'll answer it.

Prime Factorization

Square Roots: $k^2=k*k \,\!$

Common perfect square numbers:

1x1=1

2x2=4

3x3=9

4x4=16

5x5=25

6x6=36

7x7=49

8x8=64

9x9=81

10x10=100

11x11=121

12x12=144

13x13=169

14x14=196

15x15=225

16x16=256

17x17=289

18x18=324

19x19=361

20x20=400

Prime Numbers & Factors: A Prime Number is a whole number, greater than 1, that can be evenly divided only by 1 and itself. "Factors" are the numbers you multiply together to get another number.

Prime Factorization

"Prime Factorization" is finding which prime numbers you need to multiply together to get the original number.

A Great way to learn the concept of prime factorization is by creating a factor "tree" like the one below:

EXAMPLE

The prime factorization of 72:

Start by building a factor tree for 72 by dividing 72 by the smallest prime, 2.

Because 72 is 2 · 36, we write both 2 and 36 underneath the 72. Then we circle the 2 because it is prime.

Next we divide 36 by 2, writing both 2 and 18, and circling 2 because it is prime. Below the 18, we write 2 and 9, again circling the 2. Because 9 is not divisible by 2, we divide it by the next smallest prime, 3. We continue this process until all the factors in the bottom row are prime.

The prime factorization of 72 is the product of the circled factors.

72 = 2 × 2 × 2 × 3 × 3

You can also write this prime factorization SIMPLIFIED as 2³ *3 ³

Simplifying

$\sqrt{75}$

Make a factor tree.
It goes 75 the 15 times 5 equals 75, you can break down 15 into 5 times 3.
Find pairs.
Since there are no pairs, the square root is 5 times the square root of 3.
If you are not sure if the anwser is right then just type the equation in your calulator.

It's easy once you know what you are doing

Can someone check to see if this is correct? Thanks.

Some perfect squares are 2, 4, 9, 16, 25, 36, 49, 64, 81, and 100. Perfect squares are the square root of the number times itself. For example, 6*6=36. 36 is a perfect square. The square root of 36 is 6. $\sqrt{36}=6$

How to use a factor tree?

A factor tree is a way to simplify numbers.

Examples:

540

2 270 2 135 3 45 9 5 3 3 • 2,2 and 3 are prime numbers. Groups of two go out side of the square root symbol The left overs go in the square root.

Here is a video showing how to simplify division of square roots. http://www.teachertube.com/view_video.php?viewkey=c2f5900dddd0d1697425

This video was taken from Teachertube.com

Adding and simplifying square roots

$2\sqrt{3}+3\sqrt{3}=5\sqrt{3}$

Note: When you add square roots you have to have the same radicand. Just add the number in front of the radical.

Here are some steps to help you:

1) Look at your problem

$\sqrt{8}+\sqrt{50}$

2) Before you rush into adding, simplify both square roots.

$\sqrt{8}= 2\sqrt{2}$

$\sqrt{50}= 5\sqrt{2}$

3) Do the numbers in the radicands match? If they do, simply just add the numbers outside of them together.

$6\sqrt{2}+5\sqrt{2}=11\sqrt{2}$

it's really easy!

Taken from math-videos-online.com

Multiplying and Dividing Square Roots

If you are having trouble with a problem involving the multiplication or division of square roots you can put the numbers being multiplied or divided together under the square root symbol, or separate them to make the problem easier for you.

Example - $\sqrt{3*5}=\sqrt{3}*\sqrt{5}$ , $\sqrt{\frac{3}{5}}=\frac{\sqrt{3}}{\sqrt{5}}$

Remember this does not work for the addition or subtraction of square roots.

To multiply square roots: multiply the two radicands (numbers) together, and place them under the square root symbol. Then simplify the square root.

Example - $\sqrt{12}*\sqrt{6}=\sqrt{72}=6\sqrt{2}$

72 can be broken down to a perfect square like this: $\overbrace{2*\overbrace{6*6}^{36}}^{72}$