Parent guide · 5 min read
Square roots for kids: undoing squaring, one guess at a time
A square root asks a question the other way round. Squaring turns 8 into 64; the square root of 64 asks "which number, multiplied by itself, gives 64?" Children usually meet the √ symbol around ages 12–14, and it trips up more of them than it should, because it is often taught as a button on a calculator or a list to memorise rather than as the reverse of something they already know.
Try this tonight
5 things you can do at home
Say the question out loud
Every time the √ sign appears, read it as "what times itself makes…?" So √49 becomes "what times itself makes 49?" Children who read it as a mystery symbol guess; children who read it as a question answer it.
Write out the squares up to 12 × 12
Make a two-row strip: 1 to 12 on top, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 underneath. Read it top to bottom to square, bottom to top to take a root. Five minutes with this strip does more than a page of exercises.
Draw the square
A square with area 81 has sides of length 9, so √81 = 9. Ask your child to sketch a square, label the area inside, and find the side. The word "square" in "square root" finally has a reason to be there.
Trap the awkward ones between two neighbours
For √50, ask "which two perfect squares is 50 between?" It sits between 49 (7 × 7) and 64 (8 × 8), and much closer to 49, so the answer is a little more than 7. This estimating habit is what most school questions actually test.
Check by squaring
After any answer, square it and see whether you get the number back. 7.1 × 7.1 = 50.41, which is a touch over 50, so √50 is a touch under 7.1. Checking takes ten seconds and catches most slips.
What a square root is, in plain terms
Squaring a number means multiplying it by itself: 6 squared is 6 × 6 = 36. A square root goes back the other way: the square root of 36 is 6. The two operations undo each other, the same way adding 5 and subtracting 5 undo each other.
Numbers like 36, 49 and 64 that have a whole-number square root are called perfect squares. Most numbers are not perfect squares, so their roots are decimals that never end, such as √2 = 1.41421… Schools usually ask for an estimate or a rounded value in those cases.
A worked example: estimating √50 and using √81
Estimate √50. Since 7 × 7 = 49 and 8 × 8 = 64, the root of 50 is between 7 and 8, and because 50 is only 1 above 49, it is just over 7. Trying 7.1 gives 7.1 × 7.1 = 50.41, slightly too big, and 7.07 × 7.07 = 49.98, slightly too small, so √50 is about 7.07.
Now a word problem. A square garden has an area of 81 square metres. How much fence does it need? The side is √81 = 9 metres, and the perimeter is 4 × 9 = 36 metres. Finding the root was the first step, not the answer.
The traps: halving, adding under the sign, and the two answers
Halving: many children think √16 = 8, because they divide by 2. Checking by squaring catches it at once: 8 × 8 = 64, not 16. The root of 16 is 4.
Adding under the sign: √9 + √16 = 3 + 4 = 7, but √(9 + 16) = √25 = 5. A root does not split across an addition, so the two are different numbers. Ask your child to work both out and compare.
Two answers: 5 × 5 = 25 and so does (−5) × (−5), which is why solving x² = 25 gives x = 5 or x = −5. The symbol √25 on its own, though, means only the positive root, 5. Children often mix up these two situations.
Signs it’s time for outside help
When home help has done what it can
- Cannot say what √36 asks, only that "it is a button on the calculator".
- Answers √16 = 8 (halving) and does not check by squaring.
- Does not know the squares up to 12 × 12 and works each one out slowly.
- Writes √9 + √16 = √25, treating the root as if it splits across addition.
- Freezes on a number that is not a perfect square instead of estimating between two neighbours.
Questions parents ask
FAQ
What age do children learn square roots?
Squares appear from about age 9–10, and the √ symbol and estimating roots usually arrive around ages 12–14 (US Grade 8, England Key Stage 3, Australian Years 8–9). Exact timing depends on the curriculum.
Should my child use a calculator for square roots?
A calculator is fine for checking, but for school work the skill is knowing the answer is about 7, not typing √50 and copying 7.0710678. Estimating first, then checking with a calculator, builds the right instinct.
Why is the square root of 2 an endless decimal?
Because no fraction or finite decimal multiplied by itself makes exactly 2. Numbers like this are called irrational. At this stage it is enough to know they exist and to give an estimate, such as 1.41.
Can you take the square root of a negative number?
Not with the numbers children use at school: no real number times itself gives a negative. Older students meet a new kind of number for this in later years, but in the early years the answer is simply "there is no answer".
Further reading
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