= [(-1)^2 - (\sqrt7)^2] + [1 - (\sqrt7)^2] = (1 - 7) + (1 - 7) = -6 -6 = -12 - Sourci
Simplifying the Expression: A Complete Guide to [(-1)² − (√7)²] + [1 − (√7)²] = −12
Simplifying the Expression: A Complete Guide to [(-1)² − (√7)²] + [1 − (√7)²] = −12
Mathematics often involves unexpected twists — especially when exponents, square roots, and algebraic expressions combine in surprising ways. One such expression that commonly confuses beginners is:
[(-1)² − (√7)²] + [1 − (√7)²] = (1 − 7) + (1 − 7) = −6 − 6 = −12
Understanding the Context
At first glance, the equation appears complex, but with a step-by-step breakdown, it reveals elegant algebraic structure and straightforward simplification. In this article, we’ll explore the calculation, highlight key mathematical principles, and explain why this problem is a perfect example of applying order of operations, exponent rules, and square root properties in algebra.
Breaking Down the Expression Step-by-Step
Let’s begin with the full expression:
[(-1)² − (√7)²] + [1 − (√7)²]
![= [(-1)^2 - (\sqrt{7})^2] + [1 - (\sqrt{7})^2] = (1 - 7) + (1 - 7) = -6 -6 = -12](https://soloferat.biz.id/images/12---sqrt72--1---sqrt72--1---7--1---7---6--6---12-7754321.jpg)
Key Insights
We’ll simplify each bracketed term individually before combining them.
Step 1: Evaluate (-1)²
The square of a negative number follows the same rule as any real number:
(-1)² = (−1) × (−1) = 1
So, the first bracket becomes:
1 − (√7)²
Step 2: Simplify (√7)²
🔗 Related Articles You Might Like:
📰 Found the Ultimate One Piece R34 Trick – Watch How It Transforms Your Collection! 📰 One Piece R34 Secrets You Need to Try (But Only If You Dare) 📰 You NEVER Guessed This Massive One Piece LEGO Set – It’s bigger than Naruto’s Chops! 📰 Multiples Of 8 6682497 📰 Reo Home Listings 📰 Roblox Gift Card Balance 6764468 📰 Count On Nothing Suckers Fool Fishermen Every Single Time 1170633 📰 Jobs Report Today Us 📰 Sources Confirm Web Hosting Sites Comparison And The World Watches 📰 Is Rosetta Lenoire Saving Faces Or Destroying Careers With One Secret 3042450 📰 Piazza Roma Water Pump 📰 Tax Submit Deadline 📰 What Is Normalization 📰 March Sign 1183340 📰 Munting 6315701 📰 What Is Mmc 📰 Best Gameboy Advance Games 295769 📰 Finally Released The 75 Hard App Thats Taking Over Fitness Forever 4022411Final Thoughts
By definition, squaring a square root cancels out:
(√7)² = 7
Now the first bracket is:
1 − 7 = −6
Step 3: Evaluate the Second Bracket [1 − (√7)²]
We already found (√7)² = 7, so:
1 − 7 = −6
Step 4: Add Both Brackets Together
Now substitute both simplified brackets:
(−6) + (−6) = −12
Thus:
[(-1)² − (√7)²] + [1 − (√7)²] = −6 + (−6) = −12
Key Algebraic Insights
This problem demonstrates several fundamental concepts:
