Question

3. Pablo found the length of the hypotenuse of a right triangle to be √45. Can the length be simplified? Explain.

Answer 1

Yes,
`3√(5)`

Explanation:

The root is distibutive respect to the division and multiplication.

So, we need to find numbers that multiplied between then, results in 45. This is called decomposition.

`(45)/(5)=9` ⇒
`(9)/(3) =3`⇒
`(3)/(3) =1`

Then, 45 can be re-writed like 5*3*3

Now, replaced looks like this:
`√(5*3*3)  = √(5*9)` but we know that:
`√(9) =3` so, the 3 goes out of the root and the final result is:
`3√(5)`