A = \sqrt21(21 - 13)(21 - 14)(21 - 15) = \sqrt21 \cdot 8 \cdot 7 \cdot 6

Unlock the Power of Square Roots: Solve A = √[21(21 – 13)(21 – 14)(21 – 15)] with Confidence

Mathematics often presents challenges in the form of elegant algebraic expressions—like the powerful cancellation technique behind the square root equation:
A = √[21(21 – 13)(21 – 14)(21 – 15)]

At first glance, this may look like a standard expression, but it reveals a deeper mathematical insight involving factoring, simplification, and clever substitution. Let’s unpack this expression step-by-step to uncover how it simplifies effortlessly—and why it matters.

Understanding the Context

Breaking Down the Expression: A = √[21(21 – 13)(21 – 14)(21 – 15)]

Start by calculating each term inside the parentheses:

21 – 13 = 8
21 – 14 = 7
21 – 15 = 6

Solved square root multiplication: Basic Simplify: 21⋅3 | Chegg.com

Image Gallery

$SOLVED:Evaluate \int_{1}^{3} \frac{d x}{\sqrt{x^{4}+4 x^{2}+3}} \cdot ...$

$inequality - $\frac{1}{15}$

$If \( \frac{1}{2 \cdot 3^{10}}+\frac{2}{2^{2} \cdot 3^{9}}+\frac{3}{2 ...$

Solved: Resolvendo a expressão abaixo, marque a alternativa correta: 5 ...

Key Insights

So the expression becomes:
A = √[21 × 8 × 7 × 6]

Instead of leaving it as a product of four numbers, we simplify by reordering and grouping factors:

A = √(21 × 8 × 7 × 6) = √[21 × 7 × 8 × 6]

Notice the pairing: 21 and 7 are multiples, and 8 and 6 share common structure. This sets the stage for factoring to reveal perfect squares—the key to simplifying square roots.

🔗 Related Articles You Might Like:

📰 - 50 = 70 📰 So, $ \boxed{70} $ leaves are undamaged. 📰 Question: A robot follows a path marked by tiles numbered consecutively starting from 1. What is the 50th number on the list? 📰 Transform Your Driving Experiencediscover The Mychevrolet App Lvre Secret Features 7745368 📰 Discover The Secret That Glows Like A Butterfly Pea Flower Tea Magic You Never Knew You Needed 5766669 📰 Weather 77379 914018 📰 Samsung Stock Dollars 2418988 📰 Pacers Shocking Stats Shatter Thunders Champions Myth 1070533 📰 The Pietas Silent Scream Witness Picassos Unseen Grief Transfixed In Every Brushstroke 4519365 📰 7 Inches In Cm 4758819 📰 No More Gothrough The Paperworkcredly Shatters The Illusion Of Legit With Shocking Results 1449987 📰 Steam Funds Add 📰 2025 Direct Deposit Schedule 📰 Is This Oil So Miraculous Itll Change Your Life Forever 607038 📰 Viral Moment Bofa Internships And It Goes Global 📰 What Does Passion Mean 📰 This Forgotten Irish Blessing Has Been Hidden In Plain Sightimagine Its Power 1680015 📰 Unlock Seamless Communication How An Integrated Soa Gateway Revolutionizes Your Business 4805210

Final Thoughts

Step 1: Factor and Rearrange

Let’s factor each number into primes:

21 = 3 × 7
8 = 2³
7 = 7
6 = 2 × 3

Putting it all together:
A = √[(3 × 7) × (2³) × (7) × (2 × 3)]

Now combine like terms:

2³ × 2 = 2⁴ (since 2³ × 2 = 2⁴ = 16)
3 × 3 = 3²
7 × 7 = 7²

So the radicand becomes:
A = √(2⁴ × 3² × 7²)

Step 2: Extract Perfect Squares

Using the property √(a×b) = √a × √b, we separate each squared term:

A = √(2⁴) × √(3²) × √(7²)