What is -7 squared? It equals 49, because multiplying -7 by -7 gives a positive result.
If you’ve ever been tripped up by negative signs in math, you’re not alone. Squaring looks simple, yet one tiny symbol can flip an answer. This page clears it up quickly, then shows the rule behind it so you can spot the right sign each time.
By the end, you’ll know the answer, know why it works, and know how to type it without slips again.
| Number | Squared | Result |
|---|---|---|
| -10 | (-10)2 | 100 |
| -7 | (-7)2 | 49 |
| -3 | (-3)2 | 9 |
| -1 | (-1)2 | 1 |
| 0 | 02 | 0 |
| 1 | 12 | 1 |
| 3 | 32 | 9 |
| 7 | 72 | 49 |
| 10 | 102 | 100 |
What Is -7 Squared? Step-By-Step In Plain Numbers
Squaring a number means multiplying it by itself. So you take the same value twice and multiply:
- Start with the number: -7
- Write it as a product: (-7) × (-7)
- Multiply 7 × 7 to get 49
- Track the signs: negative × negative becomes positive
That’s it: (-7) × (-7) = 49. When you square any real number, the result can’t be negative.
Why A Negative Times A Negative Turns Positive
This rule isn’t a random trick. It keeps arithmetic consistent. Here’s a quick way to see it using a simple pattern.
Start with multiples of -7:
- (-7) × 3 = -21
- (-7) × 2 = -14
- (-7) × 1 = -7
- (-7) × 0 = 0
Each time the second factor drops by 1, the product increases by 7. Keep that pattern going:
- (-7) × (-1) must be 7
- (-7) × (-2) must be 14
- (-7) × (-3) must be 21
So negative × negative lands on a positive number. Squaring -7 uses that same rule, so the sign flips to positive and the magnitude is 7 × 7.
Parentheses Change The Meaning More Than You Think
Most wrong answers come from mixing up these two expressions:
- (-7)2 means “square the whole number -7.” Result: 49.
- -72 means “square 7, then apply the negative sign.” Result: -49.
See the difference? Parentheses decide whether the negative sign is part of the base. In many textbooks and calculators, exponents are applied before a leading negative sign unless parentheses force the sign into the base.
How To Read It Out Loud
A neat habit: say what you see.
- (-7)2 → “negative seven, squared”
- -72 → “negative of seven squared”
That tiny shift in wording keeps your brain from sliding past the parentheses.
Fast Checks That Catch Sign Errors
When you’re moving quickly, use two quick checks that don’t need extra work.
Check 1: Squares Can’t Be Negative
If you truly squared a real number, your answer should be 0 or positive. If you got a negative result, you likely squared first and then applied a negative sign, or you dropped parentheses.
Check 2: Estimate The Size
7 squared is 49. So the square of -7 must land at the same size as 7 squared. If your answer is 14, 7, or 21, you multiplied instead of squaring. If your answer is 343, you cubed it.
Calculator And Typing Entry Tips
Different tools read negatives and exponents in slightly different ways. You can dodge headaches with one habit: use parentheses whenever the base is negative.
- On most scientific calculators, type (–7)x² to get 49.
- On a phone calculator with a power button, type (-7)^2 or use parentheses around -7.
- In many coding languages, write (-7)**2 or pow(-7, 2).
If you want a quick confirmation, you can plug (-7)^2 into Wolfram|Alpha and see the result immediately.
What Squaring Means In Geometry And Graphs
Squaring shows up in more places than drill problems. It connects to distance, area, and curves.
Area: The Square Of A Side Length
A square with side length 7 has area 49 square units. A “length” can’t be negative in geometry, yet the algebra still lines up: the square wipes out the sign and keeps the size.
Distance: Negative Directions Still Give Positive Distance
On a number line, -7 is 7 units from 0. Distance uses absolute size, not direction. Squaring behaves in a similar way: it removes the sign and keeps the magnitude.
Graphs: Why y = x² Sits Above The Axis
In the graph of y = x², both x = 7 and x = -7 map to y = 49. That symmetry is a visual reminder that squaring treats +7 and -7 as equals in size.
Common Mix-Ups With -7 Squared And Close Variations
Let’s pin down the usual traps, since they’re the reason this topic keeps popping up in homework and quizzes.
Mix-Up: Confusing Squaring With Doubling
Doubling -7 gives -14. Squaring -7 gives 49. The operations feel similar when you’re tired, so it helps to write the multiplication sign at least once: (-7) × (-7).
Mix-Up: Treating The Negative Sign Like A Decoration
A leading negative sign matters. If the expression is (-7)², the negative sign sits inside the base. If it’s -7², the negative sign sits outside the exponent. Parentheses show where the sign belongs.
Mix-Up: Mixing Up Exponent Rules With Order Of Operations
Order of operations tells you when to apply exponents. Exponents happen before a leading negative sign unless parentheses force the negative into the base. If you want a crisp refresher, Khan Academy’s page on multiplying negative numbers is a solid reference.
Practice Problems To Lock It In
Doing a few quick reps makes the rule stick. Try these without a calculator first, then check yourself.
- Compute (-5)².
- Compute -5².
- Compute (-7)².
- Compute -7².
- Compute (-7)³.
- Compute (-7) × 7.
- Compute (-(7))².
Work each one by writing it as multiplication. Then circle the sign you expect before you multiply.
How To Handle Exponents With A Leading Minus Sign
Math uses the same symbol “-” for two different jobs: subtraction and a negative sign. With exponents, that can cause a silent slip.
When you see -7, you’re looking at a negative number. When you see 0 – 7, you’re looking at subtraction. On paper, they look similar. In an expression like -72, the minus sign is a leading sign, not part of the exponent itself.
That’s why order of operations matters. Exponents apply to the base right next to them. A leading minus sign is applied after the exponent unless you use parentheses. So:
- -72 becomes -(72) which is -49
- (-7)2 keeps the minus sign inside the base, making the product positive: 49
If you’d like a quick mental cue, treat parentheses like a fence. If the minus sign is inside the fence with the number, it gets squared too.
Even Powers Versus Odd Powers
Squaring is an even power. That’s why the sign flips to positive. The same idea keeps working as powers grow.
Even Powers Make A Positive Result
Any negative number raised to an even power gives a positive result. The reason is simple: you’re multiplying an even count of negative factors, so the negatives pair up.
- (-7)2 = (-7) × (-7) = 49
- (-7)4 = (-7) × (-7) × (-7) × (-7) = 2401
Odd Powers Keep The Negative Sign
An odd power leaves one negative factor unpaired, so the product stays negative.
- (-7)3 = (-7) × (-7) × (-7) = -343
- (-7)5 is negative as well
This even/odd pattern is handy when the numbers get big. You can predict the sign before you do any long multiplication.
How This Shows Up In Algebra Problems
You’ll see squares of negatives in lots of standard algebra moves. Knowing where the parentheses belong saves time and prevents chain-reaction mistakes.
Solving Equations With Squares
Suppose you have x2 = 49. Two numbers square to 49: 7 and -7. That’s why many square-root steps produce a “plus or minus” result. It’s not extra work; it’s the full set of solutions.
Factoring And The Difference Of Squares
The identity a2 – b2 = (a – b)(a + b) uses squares that ignore sign. Since (-7)2 equals 72, the square terms in an expression may simplify even when the original values have different signs.
Distance Formulas And Squared Terms
In coordinate geometry, distance formulas include squared differences like (x2 – x1)2. That difference can be negative, yet squaring makes it nonnegative, which matches the idea that distance can’t be negative.
More Practice Without A Calculator
If you want the sign rules to feel automatic, mix these into your practice set. Write each one as multiplication and decide the sign before you multiply.
- (-12)2
- -122
- (-2)6
- (-2)7
- (-7)2 + (-7)
- – (72) + 7
After you compute, do a quick sanity check: any true square should be 0 or positive. If your line ends with a negative number, make sure the negative sign is outside the exponent on purpose.
How To Avoid The Most Common Test Trap
Many quizzes hide the trick in plain sight: they’ll print -72 without parentheses and see who assumes it means (-7)². Don’t guess. Mark it up.
When you see a leading minus sign and an exponent, rewrite the expression on your scratch paper in one clean line:
- If there are no parentheses, rewrite it as -(72).
- If there are parentheses, rewrite it as (-7) × (-7).
This rewrite step looks small, yet it prevents sign errors that can ripple through a longer problem. It’s the same habit programmers use when they add parentheses to make operator precedence explicit.
| Expression | Answer | Sign Cue |
|---|---|---|
| (-5)2 | 25 | Negative inside base → positive |
| -52 | -25 | Negative outside exponent → stays negative |
| (-7)2 | 49 | Negative inside base → positive |
| -72 | -49 | Negative outside exponent → stays negative |
| (-7)3 | -343 | Odd power keeps the negative |
| (-7) × 7 | -49 | One negative factor → negative |
| (-(7))2 | 49 | Still the base is -7 |
Mini Checklist For Any Negative Number Squared
When you hit a problem like this on a worksheet, run this quick checklist. It takes five seconds.
- Is the negative sign inside parentheses with the base?
- Is the exponent 2 (a square) or another power?
- Rewrite it as multiplication once: (base) × (base).
- Apply the sign rule: negative × negative becomes positive.
- Multiply the magnitudes: 7 × 7 = 49.
Answer Recap You Can Reuse
Back to the original question: what is -7 squared? With parentheses, (-7)² is the product of two negatives, so the result is 49. If you see -7² without parentheses, that’s the negative of 7 squared, so it’s -49. When in doubt, write the multiplication and let the signs do their job.