FINDING SQUARE ROOTS AND CUBE ROOTS
About "Finding square roots and cube roots"
Finding square roots and cube roots :
The square root of a positive number p is x if x² = p. There are two square roots for every positive number.
For example, the square roots of 36 are 6 and −6, because 6² = 36 and (-6)² = 36. The square roots of 1/25 are 1/5 and -1/5. We can write the square roots of 1/25 as ±1/5.
The symbol √ indicates the positive, or principal square root.
A number that is a perfect square has square roots that are integers. The number 81 is a perfect square because its square roots are 9 and −9.
The cube root of a positive number p is x if x³ = p. There is one cube root for every positive number.
For example, the cube root of 8 is 2 because 2³ = 8.
The cube root of 1/27 is 1/3, because (1/3)³ = 1/27.
The symbol ∛ indicates indicates the cube root.
A number that is a perfect cube has a cube root that is an integer.
The number 125 is a perfect cube because its cube root is 5.
Finding square roots and cube roots - Examples
Example 1 :
Solve the equation x² = 121 for "x".
Solution :
x² = 121
Solve for x by taking the square root of both sides.
x = ± √121
Apply the definition of square root.
Think: What numbers squared equal 121 ?
x = ± 11
Hence, the solutions are 11 and −11.
Example 2 :
Solve the equation x² = 16/169 for "x".
Solution :
x² = 16/169
Solve for x by taking the square root of both sides.
x = ± √(16/169)
Apply the definition of square root.
Think: What numbers squared equal 16/169 ?
x = ± 4/13
Hence, the solutions are 4/13 and −4/13.
Example 3 :
Solve the equation x³ = 729 for "x".
Solution :
x³ = 729
Solve for x by taking the cube root of both sides.
x = ∛729
Apply the definition of cube root.
Think: What number cubed equals 729 ?
x = 9
Hence, the solutions is 9.
Example 4 :
Solve the equation x³ = 8/125 for "x".
Solution :
x³ = 8/125
Solve for x by taking the cube root of both sides.
x = ∛(8/125)
Apply the definition of cube root.
Think: What number cubed equals 8/125 ?
x = 2/5
Hence, the solutions is 2/5.
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