A = \sqrt{21(21 - 13)(21 - 14)(21 - 15)} = \sqrt{21 \cdot 8 \cdot 7 \cdot 6}

February 22, 2026

$A = \sqrt{21(21 - 13)(21 - 14)(21 - 15)} = \sqrt{21 \cdot 8 \cdot 7 \cdot 6}$

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.

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

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.

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)

Now simplify:

√(2⁴) = 2² = 4
√(3²) = 3
√(7²) = 7

Multiply the results: A = 4 × 3 × 7 = 84

Why This Technique Matters for Math Students and Lifelong Learners

This example showcases a fundamental algebraic strategy: Factor first, simplify under the radical, and exploit perfect squares. These steps reduce complexity and reveal elegant answers without heavy computation.

This method is valuable not just for solving equations, but for improving conceptual understanding of square roots, factoring, and expressions—skills essential in algebra, calculus, and real-world math applications like physics, engineering, and data science.

Final Answer

A = √[21(21 – 13)(21 – 14)(21 – 15)] = √(21 × 8 × 7 × 6) = √(2⁴ × 3² × 7²) = 2² × 3 × 7 = 4 × 3 × 7 = 84

So, A = 84

Try practicing similar problems—mastering square roots starts with understanding simplification. Whether for school, test prep, or personal enrichment, this technique ensures faster, stress-free solutions. Keep exploring the symmetry and patterns in algebra—your future math confidence depends on it!

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Meta Description: Unlock the secret to simplifying complex square roots with step-by-step explanation of A = √[21(21 – 13)(21 – 14)(21 – 15)]. Learn how factoring and perfect squares make solving √(21×8×7×6) a breeze—perfect for students and math enthusiasts.