Mathematics is a subject that often intimidates many, but it doesn’t have to be that way. With the right tricks and shortcuts, you can simplify complex calculations and make math more approachable and even enjoyable.

**Squaring Numbers**

Squaring a number means multiplying the number by itself. This can also be called ‘a number squared’. The symbol for squared is ².

While this might seem straightforward for smaller numbers, larger numbers can be more challenging. Here are some tricks to make squaring numbers easier:

**Trick 1: Squaring Numbers Ending in 5**

For any two-digit number ending in 5 (e.g., 15, 25, 35), you can quickly find its square using a simple trick:

- Remove the 5 at the end.
- Multiply the remaining digit(s) by itself plus one.
- Append 25 to the result.

**Example: Square of 25**

Step 1: Remove the 5: We get 2.

Step 2: Multiply 2 by (2 + 1): 2×3=6.

Step 3: Append 25: The square of 25 is 625.

**Trick 2: Using the Difference of Squares**

The difference of squares formula states that (a + b)² = a² + b² + 2ab or (a – b)² = a² + b² – 2ab. The form where ‘b’ has a smaller value should be preferred. This can be useful for squaring numbers close to a base number.

**Example: Square of 48**

Step 1: Recognize that 48=50-2.

Step 2: Use the formula: (50−2)²=(50²+2²)−(2×50×2).

Step 3: Calculate:

- 50²=2500
- 4×50=−200
- 2²=4

Step 4: Add them up: 2500−200+4=2304.

So, 482=2304.

## Trick 3: Squaring a Three-digit Number

**Example: Square of 214**

**Step 1:** Subtract the last digit from the number being squared.

214 – 4 = 210

**Step 2: **Add the last digit to the number being squared.

214 + 4 = 218

**Step 3: **Multiply the numbers from Step 1 and Step 2.

210 x 218 = 45,780

**Step 4: **Square the last digit of the number being squared and add it to the answer from Step 3.

Since 4² = 16, we add 45,780 + 16 = 45,969.

**Finding Square Roots**

Finding square roots can be challenging without a calculator, but some tricks can simplify the process. Here is a trick to find the square roots of a large number easily.

**Trick: Estimation and Refinement**

For example, let us find the **square root of 4761.**

**Step 1:**The unit digit in this number is 9, which can be a unit digit of its square root number such as 1 or 9. Because 1² is 1 and 9² is 81.**Step 2:**Now let us consider the first two digits that is 47 which comes between the squares of 6 and 7 because 6² < 47< 7².**Step 3:**We can assume that the tens digit of the square root of 4761 is the lowest among the two numbers i.e. 6 and we need to find the unit digit of the square root of the number 4761.**Step 4:**Now, we need to find between 61 or 69 which is the square root of 4761.**Step 5:**Since the tens digit is 6 and the next number is 7, we need to multiply both the numbers like 6 x 7 = 42 and since 42 is less than 47.**Step 6:**Square root of 4489 will be the bigger number between 61 and 69 i.e. 69.

Therefore, √4761 = 69.

**Spark Math Program: Elevating Mathematical Excellence**

Mastering math shortcut tricks like squaring numbers, finding square roots, and calculating percentages not only simplifies complex calculations but also enhances overall mathematical proficiency. By practicing these techniques regularly, you’ll find yourself solving problems more efficiently whether in academic settings or real-life scenarios. So go ahead, give these tricks a try, and watch your math skills soar! The Spark Math program is a comprehensive and innovative educational initiative designed to enhance students’ mathematical skills and abilities, enabling them to excel in both academic settings and international math competitions.

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