Squaring Two-Digit Numbers

Mental Math · Axiom Academy

LESSON Squaring Two-Digit Numbers Master powerful mental math techniques to square any two-digit number quickly and accurately 1. The Foundation: Understanding Squares Before diving into advanced techniques, let's visualize what squaring really means. When we square 5, we're creating a 5×5 grid with 25 total squares. Speed: Calculate squares instantly without a calculator Patterns: Discover beautiful mathematical relationships Applications: Physics, geometry, statistics, and more 2. Technique 1: The Difference of Squares This technique works by using nearby "friendly" numbers that are easier to multiply. Let's see how to square 43 using 40 and 46 (which are 3 away from 43). Step 1: Choose distance d = 3 (easy to work with) Step 2: Find neighbors: 43 - 3 = 40 and 43 + 3 = 46 Step 3: Multiply: 40 × 46 = 1,840 (easier mental math) Step 4: Add d 2 : 1,840 + 9 = 1,849 3. Technique 2: Numbers Ending in 5 Numbers ending in 5 have a remarkably simple pattern! This is one of the fastest mental math techniques you can learn. Step 1: Identify tens digit: a = 6 Step 2: Calculate a(a+1): 6 × 7 = 42 4. Technique 3: Near Round Numbers When a number is close to a round number (like 50, 60, 100), we can use the binomial expansion to make mental math much easier. Example: Calculate 48 2 (near 50) Step 2: Apply formula: 50 2 - 2(50)(2) + 2 2 Step 3: Calculate: 2,500 - 200 + 4 Example: Calculate 73 2 (near 70) Step 2: Apply formula: 70 2 + 2(70)(3) + 3 2 Step 3: Calculate: 4,900 + 420 + 9

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