rational factor as the coefficient of the irrational factor

[blessed91]

I need help with these exercises:

Instructions: Write the rational factor as the coefficient of the irrational factor.

1) square root of 128

2) cube root of 16

 

[stapel]

Instructions: Write the rational factor as the coefficient of the irrational factor.

I've never seen this terminology before. I would guess that they're wanting you to simplify the radical expressions, taking whatever you can out of the roots. For instance:

. . . . .\(\displaystyle \L \sqrt{75}\, =\, \sqrt{(25)(3)}\, =\, \sqrt{25}\sqrt{3}\, =\, 5sqrt{3}\)

The "5" is the rational part, and the "sqrt[3]" is the irrational part.

Eliz.

 

[blessed91]

okay, but how do you know to use (25) and (3)? To get (75) I could use (15) and (5). Is it because 3 is a smaller number than 5? Thank you for your help.

 

[stapel]

how do you know to use (25) and (3)?

Experience. When in doubt, factor completely, all the way down to prime numbers.

. . . . .75 = 5 × 5 × 3

Since there are two copies of the factor "5", it comes out of the root; the "3" is stuck inside.

For further information, try here.

Eliz.