SOLUTION: These are my homework questions that I am confused on. Quetion 1 If x is any real number, is this always true? Show why or why not. square root of x^2 = x I say

Algebra ->  Expressions -> SOLUTION: These are my homework questions that I am confused on. Quetion 1 If x is any real number, is this always true? Show why or why not. square root of x^2 = x I say       Log On


   

Question 160592: These are my homework questions that I am confused on.
Quetion 1
If x is any real number, is this always true? Show why or why not.
square root of x^2 = x
I say no because if x is a negative number than the square result would not be a negative number.

Question 2
If a and b are real numbers and a^2 = b^2, explain your answer.
I say yes because if a and b are equal in the beginning, then if you do the same to each of them then they will still be equal.
Thank you for your help.
Found 2 solutions by Fombitz, MathLover1:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Question 1: Yes, you're correct.
What is true is that:
sqrt%28x%29=x and sqrt%28x%29=-x
.
.
.
Question 2: Yes, you're correct again.
If a=b
then it follows that
a%2Aa=b%2Aa
a%5E2=b%2Aa
But since a=b then you can substitute,
a%5E2=b%2Ab
a%5E2=b%5E2
.
.
.
Good job!

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

1. If x is any real number, is this always true?
answer: yes

The sqrt%28+x%5E2%29 must always by definition be x regardless if x is positive or negative number….example: %28-3%29%5E2+=+%28-3%29%28-3%29=9
2. If a and b are real numbers and a%5E2+=+b%5E2, then a=b.