Radical and its rational exponential form

Click For Summary
SUMMARY

The discussion centers on the equivalence of the expressions sqrt((-3)^2) and (-3)^2/2, highlighting a common misconception in mathematical interpretation. Participants assert that while sqrt(9) equals 3, the expression (-3)^2/2 can be misleading, particularly in the context of complex numbers. The consensus is that these forms are not universally equivalent, especially when considering the properties of square roots and the need to select specific roots in complex analysis.

PREREQUISITES
  • Understanding of square roots and their properties
  • Familiarity with complex numbers and their operations
  • Knowledge of exponentiation rules
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the properties of square roots in real and complex numbers
  • Learn about the implications of choosing roots in complex analysis
  • Explore the differences between real and complex exponentiation
  • Review algebraic identities involving squares and square roots
USEFUL FOR

Mathematics students, educators, and anyone interested in clarifying misconceptions about square roots and complex numbers.

OceanSpring
Messages
11
Reaction score
0
Can someone explain how these are equivalent.

sqrt((-3)^2) = (-3)^2/2

=sqrt(9) and (-3)^1

3 is not equal to -3

(-3)^2/2 can be expressed as:

(-3^2)^1/2 and (-3^1/2)2

(9)^1/2 and (sqrt(-1)sqrt(3))^2

3 is not equal to -3

Every textbook I've come across says these forms are equivalent. This seems totally inconsistent.
 
Last edited:
Mathematics news on Phys.org
sqrt((-3)^2) = (-3)^2/2
That is not true. This rule applies to positive numbers in the inner bracket only.

In the complex numbers, you have to choose which root you would like to take (as there are always two, apart from sqrt(0), so sqrt(9)=-3 is... well, not completely wrong, but not really right.
 

Similar threads

High School Computing a tricky complex math problem - where did I go wrong?
  • · Replies 7 ·
Replies
7
Views
1K
High School Bounds for the index of a radical
  • · Replies 7 ·
Replies
7
Views
2K
High School Generating the formula for the coefficients of an alternating series
  • · Replies 17 ·
Replies
17
Views
5K
Graduate De-Nesting Radicals: Solving & Simplifying Solutions
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Method for finding a complex series?
  • · Replies 10 ·
Replies
10
Views
2K
MHB Exponential Equation solve 54⋅2^(2x)=72^x⋅√0.5
  • · Replies 3 ·
Replies
3
Views
2K
MHB How to simplify a diabolical expression involving radicals
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Transforming coordinates between Cartesian and spherical
  • · Replies 1 ·
Replies
1
Views
2K
High School How to pick some numbers out of 13 integers, by a 4 digits code
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Math Myth: The rationals are numbers
  • · Replies 142 ·
5
Replies
142
Views
10K