SOLUTION: Give an example of numbers a and b that show {{{sqrt(A + B)}}} is not the same as {{{sqrt(A) + sqrt(B)}}}

Question 626114: Give an example of numbers a and b that show is not
the same as
Answer by Edwin McCravy(20064) (Show Source): You can put this solution on YOUR website!
Give an example of numbers a and b that show is not
the same as

Let A = 16, B = 9

 =  = 5

 +  = 4 + 3 = 7

5 does not equal 7.

---------------------------- 

Find all values of a and b that make those two expressions equal to each other.


 = 

Square both sides of the equation:

 = 

 A + B = A + 2 + B

Simplify the equation:

     0 = 2

Divide both sides by 2

     0 = 

Square both sides

    0� = 

     0 = AB

So it's only true if the product of A and B is zero.
That is to say, one or both of A and B must be equal 
to zero.
 
Edwin

RELATED QUESTIONS
Show that: if a > 0, b > 0, and sqrt{a} < sqrt{b}, then a < b. Hint given: b - a (answered by math_tutor2020)

find the value of A and B if sqrt(A) x sqrt(B) = 4 sqrt(A) - sqrt(B) =... (answered by stanbon)

If 0 < a < b, show that a < sqrt{a•b} < b. The number sqrt{a•b} is called the... (answered by math_tutor2020)

find an equation of the line that bisects the obtuse angles formed by the lines with... (answered by solver91311)

Let a, b, c, and d be distinct real numbers such that a = \sqrt{4 + \sqrt{5 + a}}, b =... (answered by CPhill,ikleyn)

If 0 < a < b, show that a < sqrt{ab} < b. Note: The number sqrt{ab} is called the... (answered by Edwin McCravy)

Rationalize the denominator..... (answered by Fombitz)

Give an example to show that sqrt{a^2} is not equal to a. Use it to explain why sqrt{a^2} (answered by mccravyedwin)

which of the following square roots is an irrational number? I got D {{{sqrt(15) }}} (answered by solver91311)