Quick question regarding simplifying |sqrt[7] - 9|

[metalmachine]

Hello all. Im in need of some help. How do I simplify

|√7 - 9|

The absolute value of the square root is throwing me off. I came up with either

9+√7

or

9 - √7

Thanks

 

[galactus]

\(\displaystyle \L\\9-\sqrt{7}\)

 

[metalmachine]

ok cool, but why?

It helps for me to understand better when I know the why.

 

[stapel]

I came up with either 9+√7 or 9 - √7

How did you arrive at "9 + sqrt[7]"? If you'd had to simplify |3 - 5|, would you have said that this equalled 5 + 3? :shock:

Consider the example above: |3 - 5|. What is the absolute value of this? How did you find this? :?:

Now relate that process to |sqrt[7] - 9|. :wink:

Eliz.

:arrow: P.S. Welcome to FreeMathHelp!

 

[metalmachine]

Thank you. Im trying to finish my math requirements so I thought a forums would be a good place to get help.

Ok...I dont know if |3-5| = 5+3. Does it = 3-5? Or does |3-5| = |3| - |5| ??

Does |√7-9| = |√7| - |9| ??

 

[stapel]

I dont know if |3-5| = 5+3.

Um... does 3 - 5 usually equal -8? Doesn't it usually equal -2? So |3 - 5| = |-2| = 2 = 5 - 3...? :shock:

...or has your class not covered absolute values yet...? :?:

Eliz.

 

[metalmachine]

I understand So |3 - 5| = |-2| = 2

What throws me off is the square root.

So |√7 - 9| = √7 - 9 ??

 

[jwpaine]

I understand So |3 - 5| = |-2| = 2

What throws me off is the square root.

So |√7 - 9| = √7 - 9 ??

Absolute value is the distance from zero:

√7 - 9 or -(√7 - 9)
√7 - 9 or -√7 + 9
√7 - 9 or 9 - √7

 

[Deleted member 4993]

When there are constants inside the |abs| operator - there is excatly one value for that. So:

|√7 - 9| = |~2.645751311 - 9| = ~6.3

Since √7 is irrational - you would only get approximate values for decimal answer. Absolute value of a constant - by definition is always positive.

 

[Denis]

and your expression could be written |sqrt(7) - sqrt(81)|