Finding the root of 75

**ariel32** · August 15th 2012, 11:54 PM

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?

**earboth** · August 16th 2012, 01:46 AM

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 $\sqrt{128} = 8 \cdot \sqrt{2}$