Squares, Cubes & Roots of Decimals

Squaring and cubing decimals, and finding square and cube roots of decimals, using the decimal-place count or by converting to fractions — with worked examples, a worksheet with memo and a quiz.

Squares, cubes and roots of decimals follow directly from the multiplication rule you already know: do the whole-number version, then count the decimal places.

1Squaring and cubing decimals

Worked ExampleCalculate: 0,2² and 0,3³

1
0,2² means 0,2 × 0,2. Whole numbers: 2 × 2 = 4.
2
Decimal places: 1 + 1 = 2 → 0,04.
Not 0,4 — count carefully.
3
0,3³ = 0,3 × 0,3 × 0,3. Whole numbers: 3 × 3 × 3 = 27; places: 1+1+1 = 3 → 0,027.
Three decimal places because three numbers were multiplied.

⚠️

0,2² is not 0,4. Squaring a decimal between 0 and 1 makes it smaller: 0,2² = 0,04. Count the decimal places every time.

2Square roots of decimals

The safest method is to turn the decimal into a fraction, root the top and bottom, then convert back.

Worked ExampleCalculate: 0,25

1
Write as a fraction: 0,25 = 25100.
Two decimal places → denominator 100.
2
25100 = 25 / 100 = 510.
Root the top and the bottom.
3
= 0,5.
Check: 0,5 × 0,5 = 0,25. ✓

Worked ExampleCalculate: 0,16

1
0,16 = 16100.
2
16 / 100 = 410 = 0,4.
3
Check: 0,4 × 0,4 = 0,16. ✓
Always square your answer back to be sure.

3Cube roots of decimals

Worked ExampleCalculate: 0,008

1
0,008 = 81000.
Three decimal places → denominator 1000.
2
8 / 1000 = 210.
3
= 0,2. Check: 0,2 × 0,2 × 0,2 = 0,008. ✓

💡

The check is the exam technique: after any root, multiply your answer back. It takes seconds and it is the only way to be certain the decimal point is in the right place.