About square & cube root calculator
A square root is the number that, multiplied by itself, gives the original. A cube root is the number that gives it when multiplied three times.
Examples
√144 = 12 because 12 × 12 = 144. The cube root of 27 is 3. Most numbers have irrational roots such as √2 = 1.41421…, which never end.
Estimating by hand
Find the perfect squares on either side. √50 lies between √49 = 7 and √64 = 8, close to 7.07.
A worked example
√200 is about 14.142, since 14² = 196 and 15² = 225. The cube root of 64 is 4. The square root of 0.25 is 0.5, because a decimal below 1 has a larger root than itself.
Simplifying roots
√72 = √(36 × 2) = 6√2. Splitting out the largest perfect square lets you write roots neatly in exams.
