A square root undoes squaring: √64 = 8 because 8² = 64. A cube root undoes cubing: ∛125 = 5 because 5³ = 125. Every positive number has two square roots, such as 8 and −8, but √ means the positive one.
Some roots are not whole numbers or fractions. √2 = 1.41421… goes on forever without repeating, so it is irrational. You can estimate it: √50 is between √49 = 7 and √64 = 8, closer to 7. Numbers like π are irrational too.
Worked example
Between which two whole numbers does √90 lie?
- 9² = 81 and 10² = 100.
- 90 is between 81 and 100.
Answer:between 9 and 10
Key words
- square root
- a number that squares to the given number
- cube root
- a number that cubes to the given number
- irrational
- cannot be written as a fraction
Practise this
New questions every time.
Common Core-referenced: 8.EE.A.2, 8.NS.A.1