Square roots and the ± sign after PSLE is a useful post-PSLE Mathematics bridge because it makes one familiar idea precise before Secondary 1 combines more symbols, faster working and less room for guesswork.
The wider route begins with After PSLE — Should My Child Start Secondary 1 Maths Early?. If a mistake keeps returning, the Punggol Mathematics diagnostic guide helps identify whether the difficulty is fluency, interpretation, strategy or execution.
At eduKatePunggol, Mathematics is taught in focused small groups of up to three students in 1.5-hour lessons near Punggol MRT. The goal is not to rush ahead, but to make the important connection stable enough that later algebra feels familiar.
WhatsApp eduKatePunggol about a post-PSLE Mathematics transition plan
The short answer: √25 names one number, but x² = 25 asks for every number that works
The symbol √25 means the principal square root of 25, which is 5.
But the equation x² = 25 asks which values of x produce 25 when squared. Both 5² and (-5)² equal 25, so the solutions are x = 5 and x = -5.
Why the square-root symbol does not mean ± automatically
The radical symbol √a is defined to represent the non-negative square root when a is non-negative.
So √9 = 3, not ±3. The ± appears when solving an equation such as x² = 9 because we are finding all values whose square is 9.
Worked example: √49
√49 = 7 because 7 is the non-negative number whose square is 49.
The number -7 also has square 49, but it is not the value of the principal square-root expression √49.
Worked example: x² = 49
Now the task changes. We need every x satisfying the equation.
x = 7 works and x = -7 works.
Therefore x = ±7.
Brackets protect negative bases
(-4)² = 16 because the whole negative number is squared.
This connects to careful substitution of signed values and to the distinction between a negative sign and a squared base.
Perfect squares make good anchors
- 1² = 1
- 2² = 4
- 3² = 9
- 4² = 16
- 5² = 25
- 6² = 36
- 7² = 49
- 8² = 64
- 9² = 81
- 10² = 100
Knowing common perfect squares makes roots easier to recognise and gives useful reasonableness checks.
Not every square root is a whole number
√20 is not a whole number because 4² = 16 and 5² = 25.
So √20 lies between 4 and 5. A calculator can approximate it, but the exact expression √20 may be the preferred form depending on the question.
A reasonableness check
If √50 is entered and a calculator returns about 7.07, the answer makes sense because 7² = 49 and 8² = 64.
That estimate is more useful than trusting the screen without context.
A square-root routine
- Ask whether the task is evaluating √a or solving x² = a.
- For √a, use the principal non-negative root.
- For x² = a with a positive, test both positive and negative roots.
- Use brackets around negative bases.
- Estimate between nearby perfect squares when needed.
Independent practice with answers
- Find √64.
- Solve x² = 64.
- Find √100.
- Solve x² = 9.
- Between which two integers does √30 lie?
Answers: 8; x = ±8; 10; x = ±3; between 5 and 6.
Frequently asked questions
Why is √25 not ±5?
Because the radical symbol denotes the principal non-negative square root.
Why does x² = 25 have two solutions?
Because both 5 and -5 produce 25 when squared.
What should students read next?
Continue to Squares, Cubes and Roots After PSLE.
Continue through the post-PSLE Mathematics route
- After PSLE — Should My Child Start Secondary 1 Maths Early?
- Secondary 1 Math Readiness Checklist After PSLE
- Squares, Cubes and Roots After PSLE
The post-PSLE period is best used to make meanings cleaner, not to race through chapters. A child who can explain the relationship is much better prepared for new notation later.
