# Finding the root of 75

• Aug 15th 2012, 11:54 PM
ariel32
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?
• Aug 16th 2012, 01:46 AM
earboth
Re: Finding the root of 75
Quote:

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: $\sqrt{9} = 3~or~\sqrt{\frac4{25}}=\frac25$

2. If the number is not a square (75 is not a square of a rational number) you can express $\sqrt{75}$ 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:

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

Since 64 is the greatest square you'll get $\sqrt{128} = 8 \cdot \sqrt{2}$
• Aug 16th 2012, 05:34 PM
hacker804
Re: Finding the root of 75
$\sqrt{75}=\sqrt{3\cdot5\cdot 5}$
$\sqrt{3\cdot5^{2}}$
$5\sqrt{3}$
• Aug 17th 2012, 11:41 PM
kalwin
Re: Finding the root of 75
Rewrite each as a multiple of a square:
√(25 * 3)
√25 * √3
5√3