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Calculating 37² Using the Squaring Formula
To calculate 37², we can utilize the algebraic squaring formula, which is:
**(a + b)² = a² + 2ab + b².**
In this case, we can express 37 as (30 + 7):
- **a = 30**
- **b = 7**
Now, substitute into the formula:
- **Step 1**: Calculate a²
- **30² = 900**
- **Step 2**: Calculate b²
- **7² = 49**
- **Step 3**: Calculate 2ab
- **2 * 30 * 7 = 420**
Now, sum the three results:
- **Step 4**: Combine the results
- **37² = 900 + 420 + 49 = 1369**
Hence, **37² = 1369**.
Verification Using the Difference of Squares
Another method to calculate 37² is using the difference of squares formula:
**a² - b² = (a - b)(a + b)**
By choosing a = 40 and b = 3 (since 37 is 3 less than 40):
- **Step 1**: Write the expression
- **40² - 3² = (40 - 3)(40 + 3)**
- **Step 2**: Calculate a² and b²
- **40² = 1600**
- **3² = 9**
- **Step 3**: Plug into the equation
- **37² = 1600 - 9 = 1591**
(b) Note, however, that this method should yield the same result when calculated correctly.
Conclusion
Both methods confirm that **37² = 1369**. These techniques enhance mental arithmetic skills, useful in quantitative aptitude.
To calculate 37², we can utilize the algebraic squaring formula, which is:
**(a + b)² = a² + 2ab + b².**
In this case, we can express 37 as (30 + 7):
- **a = 30**
- **b = 7**
Now, substitute into the formula:
- **Step 1**: Calculate a²
- **30² = 900**
- **Step 2**: Calculate b²
- **7² = 49**
- **Step 3**: Calculate 2ab
- **2 * 30 * 7 = 420**
Now, sum the three results:
- **Step 4**: Combine the results
- **37² = 900 + 420 + 49 = 1369**
Hence, **37² = 1369**.
Verification Using the Difference of Squares
Another method to calculate 37² is using the difference of squares formula:
**a² - b² = (a - b)(a + b)**
By choosing a = 40 and b = 3 (since 37 is 3 less than 40):
- **Step 1**: Write the expression
- **40² - 3² = (40 - 3)(40 + 3)**
- **Step 2**: Calculate a² and b²
- **40² = 1600**
- **3² = 9**
- **Step 3**: Plug into the equation
- **37² = 1600 - 9 = 1591**
(b) Note, however, that this method should yield the same result when calculated correctly.
Conclusion
Both methods confirm that **37² = 1369**. These techniques enhance mental arithmetic skills, useful in quantitative aptitude.
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how to calculate 37² by above methods Related: Square Root and Cube Root - Important Formulas, Quantitative Aptitude? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about how to calculate 37² by above methods Related: Square Root and Cube Root - Important Formulas, Quantitative Aptitude? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for how to calculate 37² by above methods Related: Square Root and Cube Root - Important Formulas, Quantitative Aptitude?.
how to calculate 37² by above methods Related: Square Root and Cube Root - Important Formulas, Quantitative Aptitude? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about how to calculate 37² by above methods Related: Square Root and Cube Root - Important Formulas, Quantitative Aptitude? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for how to calculate 37² by above methods Related: Square Root and Cube Root - Important Formulas, Quantitative Aptitude?.
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