radicals

[ree]

Is the square root of x squared = x (true for all values of x)? Please explain. I am so confused.

 

[stapel]

What values for "x" have you tried? What results have you obtained?

Eliz.

 

[ree]

In my opinion, yes. If 12 squared is 144 and x is 12 then it is true. Same for x = 4 then 4 squared is 16, therefore anything squared has a true value. I just wasn't sure that I understood what this meant. I thought the answer might be /x/?

 

[stapel]

If 12 squared is 144 and x is 12 then it is true. Same for x = 4 then 4 squared is 16, therefore anything squared has a true value.

You tried only whole numbers and only positive numbers, and on that basis concluded that the relation was always true for all types of numbers...?

You might want to try some different types of numbers. Fractions (particularly less than 1), negatives, and zero are frequently useful choices when examining questions of this sort.

Eliz.

 

[Guest]

I agree with stapel. While your conjecture isn't completely unfounded, it's wise to test your rule in other mediums... or you can express it as, say, (√x)² = x for all positive integers for x.

Does that make any sense?

 

[skeeter]

\(\displaystyle sqrt{x^2} = x\) is only true for values of x > 0.

\(\displaystyle sqrt{x^2} = |x|\) is true for all x.

 

[Guest]

\(\displaystyle sqrt{x^2} = x\) is only true for values of x > 0.

\(\displaystyle sqrt{x^2} = |x|\) is true for all x.

Thank you for making what I was trying to say clearer.