Square Root And Cube Root

Square Root And Cube Root – Aptitude Test Shortcuts PDF Materials

 Square roots:

  • Square root of x is r such that r2=x
  • Every positive real number has two square roots, one positive and the other negative. For example, square roots of 16 are 4 and −4 because 42=(−4)2=16
  • The positive square root is known as the principal square root and denoted by a radical sign. For example, principal square root of 16 can be given by
  • 16=4(alternatively, this can be expressed as 161/2=4)
  • The other square root of 16 can be given as
  • −16=−4
  • If we want to indicate that we are referring to both positive and negative square roots, it can be done by adding the symbol ± in front of radical sign. For example, both the square roots of 16 can be represented by
  • ±16=±4=4 or −4
  • Every negative number has two two imaginary square roots. For example, square roots of −16 are 4i and −4i, where i=−1 Note that zero has only one square root.2.

Cube roots:

  • Cube root of x is r such that r3=x and cube root is denoted using the symbol 3
  • Every real number has exactly one real cube root. For example,
  • 273=3,because 33=27−273=−3,because (−3)3=−27
  • Every non-zero real number has one real cube root and two complex cube roots. For example, all the three cube roots of 1 are 1,(−12+i32),(−12−i32)
  • Zero has only one cube root

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