# Thread: Finding the root of 75

1. ## Finding the root of 75

I have been told that in order to find the root of 75 you need to factor it
and then do 5 times root of 3 or something like that
anyway why cant i just break 75 into 2 times 35 and so on?
in any case in simple terms can you explain it?

2. ## Re: Finding the root of 75

Originally Posted by ariel32
I have been told that in order to find the root of 75 you need to factor it
and then do 5 times root of 3 or something like that
anyway why cant i just break 75 into 2 times 35 and so on?
in any case in simple terms can you explain it?
1. You can easily calculate the square-root of a number if this number is a square: $\displaystyle \sqrt{9} = 3~or~\sqrt{\frac4{25}}=\frac25$

2. If the number is not a square (75 is not a square of a rational number) you can express $\displaystyle \sqrt{75}$ as an approximation in decimal form. You have then a result with a lot of digits - and it is still not accurat!

Therefore you try to split a number into a product of a square (the square should be as large as possible) and another rational number. So you are able to calculate the square-root at least from the square. The other number remains under the root sign.

Example:

$\displaystyle \sqrt{128} = \sqrt{4 \cdot 32} = \sqrt{16 \cdot 8} = \sqrt{64 \cdot 2}$

Since 64 is the greatest square you'll get $\displaystyle \sqrt{128} = 8 \cdot \sqrt{2}$

3. ## Re: Finding the root of 75

$\displaystyle \sqrt{75}=\sqrt{3\cdot5\cdot 5}$
$\displaystyle \sqrt{3\cdot5^{2}}$
$\displaystyle 5\sqrt{3}$

4. ## Re: Finding the root of 75

Rewrite each as a multiple of a square:
√(25 * 3)
√25 * √3
5√3