© 2014 Shmoop University, Inc. All rights reserved.
Basic Operations

Basic Operations

Roots are sort of like the opposites of powers

The square root of 9, written as 9^1/2, means "what number times itself gives an answer of 9?"  

  • 3 squared, or 3 to the second power (3 x 3) is 9
  • So, the square root of 9 is 3

The cube root of 8, written as 8^1/3, means "what number times itself three times is 8?" 

  • 2 cubed, or 2 to the third power (2 x 2 x 2) is 8
  • So, the cube root of 8 is 2

Roots can also be written as exponents. 

 The square root can be written as something raised to the power of 1/2, while a cube root is written as something raised to the power of 1/3. For example, 625^1 / 4 can be written as 625^(1/4)

  • Since 5 x 5 x 5 x 5 is 625625^1 / 4 = 5.

Look Out: Order of operation (PEMDAS) always applies, so when there is an operation to simplify underneath the root symbol, simplify the operation, then take the root.

You cannot take the square root of a negative number.

A number times itself could never be negative. So, there is no answer to the problem (-49)^1/2 , since 7 x 7 = +49 and -7 x -7 = +49 too. 

However, you can take the cube root of a negative number

The cube root of -27 is -3 (-27^1/3 = -3), since -3 x -3 x -3 = -27.

Advertisement
Advertisement
Advertisement