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2026-01-01
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2026-02-28
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<p>132 Learners</p>
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<p>Last updated on<strong>August 30, 2025</strong></p>
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<p>Last updated on<strong>August 30, 2025</strong></p>
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<p>The mathematical operation of finding the difference between two irrational numbers is known as the subtraction of irrational numbers. This operation is essential for simplifying expressions and solving problems that involve irrational numbers, which cannot be expressed as simple fractions.</p>
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<p>The mathematical operation of finding the difference between two irrational numbers is known as the subtraction of irrational numbers. This operation is essential for simplifying expressions and solving problems that involve irrational numbers, which cannot be expressed as simple fractions.</p>
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<h2>What is Subtraction of Irrational Numbers?</h2>
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<h2>What is Subtraction of Irrational Numbers?</h2>
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<h2>How to Subtract Irrational Numbers?</h2>
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<h2>How to Subtract Irrational Numbers?</h2>
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<p>When subtracting irrational<a>numbers</a>, follow these steps:</p>
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<p>When subtracting irrational<a>numbers</a>, follow these steps:</p>
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<p>Align the numbers: Write the numbers in a way that is easy to compare, especially if they involve similar radicals.</p>
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<p>Align the numbers: Write the numbers in a way that is easy to compare, especially if they involve similar radicals.</p>
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<p>Simplify radicals: Ensure the radicals are simplified as much as possible to identify any potential like terms.</p>
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<p>Simplify radicals: Ensure the radicals are simplified as much as possible to identify any potential like terms.</p>
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<p>Perform<a>subtraction</a>: Subtract the simplified forms, being careful with signs and ensuring<a>accuracy</a>in calculations.</p>
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<p>Perform<a>subtraction</a>: Subtract the simplified forms, being careful with signs and ensuring<a>accuracy</a>in calculations.</p>
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<h2>Methods to Subtract Irrational Numbers</h2>
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<h2>Methods to Subtract Irrational Numbers</h2>
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<p>The following methods can be used for the subtraction of irrational numbers:</p>
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<p>The following methods can be used for the subtraction of irrational numbers:</p>
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<p><strong>Method 1: Simplification Method</strong></p>
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<p><strong>Method 1: Simplification Method</strong></p>
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<p>To use the simplification method in subtracting irrational numbers, follow these steps:</p>
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<p>To use the simplification method in subtracting irrational numbers, follow these steps:</p>
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<p><strong>Step 1:</strong>Simplify the radicals in each number as much as possible.</p>
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<p><strong>Step 1:</strong>Simplify the radicals in each number as much as possible.</p>
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<p><strong>Step 2:</strong>Arrange any like terms involving similar radicals.</p>
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<p><strong>Step 2:</strong>Arrange any like terms involving similar radicals.</p>
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<p><strong>Step 3:</strong>Subtract the like terms.</p>
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<p><strong>Step 3:</strong>Subtract the like terms.</p>
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<p>For example, subtract √18 from √50:</p>
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<p>For example, subtract √18 from √50:</p>
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<p><strong>Step 1:</strong>Simplify √18 to 3√2 and √50 to 5√2.</p>
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<p><strong>Step 1:</strong>Simplify √18 to 3√2 and √50 to 5√2.</p>
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<p>Step 2: Align like terms: 5√2 - 3√2.</p>
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<p>Step 2: Align like terms: 5√2 - 3√2.</p>
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<p><strong>Step 3:</strong>Perform subtraction: 2√2.</p>
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<p><strong>Step 3:</strong>Perform subtraction: 2√2.</p>
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<p><strong>Method 2: Decimal Approximation</strong></p>
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<p><strong>Method 2: Decimal Approximation</strong></p>
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<p>In some cases, especially when precision is less critical, you can approximate irrational numbers as<a>decimals</a>and subtract them.</p>
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<p>In some cases, especially when precision is less critical, you can approximate irrational numbers as<a>decimals</a>and subtract them.</p>
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<p>For example, subtract π (approximately 3.14159) from √10 (approximately 3.16228):</p>
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<p>For example, subtract π (approximately 3.14159) from √10 (approximately 3.16228):</p>
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<p>Solution: 3.16228 - 3.14159 = 0.02069</p>
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<p>Solution: 3.16228 - 3.14159 = 0.02069</p>
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<h3>Explore Our Programs</h3>
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<h2>Properties of Subtracting Irrational Numbers</h2>
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<h2>Properties of Subtracting Irrational Numbers</h2>
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<p>Subtracting irrational numbers has some characteristic properties:</p>
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<p>Subtracting irrational numbers has some characteristic properties:</p>
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<p>Not commutative The order of subtraction matters; changing it will alter the result,<a>i</a>.e., A - B ≠ B - A.</p>
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<p>Not commutative The order of subtraction matters; changing it will alter the result,<a>i</a>.e., A - B ≠ B - A.</p>
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<p>Not associative Grouping changes the result when three or more numbers are involved, i.e., (A - B) - C ≠ A - (B - C).</p>
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<p>Not associative Grouping changes the result when three or more numbers are involved, i.e., (A - B) - C ≠ A - (B - C).</p>
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<p>Subtracting zero leaves the number unchanged Subtracting zero from any irrational number results in the same number: A - 0 = A.</p>
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<p>Subtracting zero leaves the number unchanged Subtracting zero from any irrational number results in the same number: A - 0 = A.</p>
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<h2>Tips and Tricks for Subtracting Irrational Numbers</h2>
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<h2>Tips and Tricks for Subtracting Irrational Numbers</h2>
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<p>Here are some tips for efficiently subtracting irrational numbers:</p>
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<p>Here are some tips for efficiently subtracting irrational numbers:</p>
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<p>Tip 1: Simplify radicals whenever possible to see if subtraction can be performed directly.</p>
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<p>Tip 1: Simplify radicals whenever possible to see if subtraction can be performed directly.</p>
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<p>Tip 2: Use decimal approximations for quick estimates when precise values are not necessary.</p>
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<p>Tip 2: Use decimal approximations for quick estimates when precise values are not necessary.</p>
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<p>Tip 3: Use a<a>calculator</a>for complex calculations to avoid manual errors.</p>
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<p>Tip 3: Use a<a>calculator</a>for complex calculations to avoid manual errors.</p>
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<h2>Forgetting to Simplify Radicals</h2>
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<h2>Forgetting to Simplify Radicals</h2>
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<p>Students sometimes perform subtraction without simplifying the radicals first. Always simplify to ensure accuracy and identify like terms.</p>
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<p>Students sometimes perform subtraction without simplifying the radicals first. Always simplify to ensure accuracy and identify like terms.</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Simplify the radicals: √8 = 2√2 and √18 = 3√2. Subtract: 3√2 - 2√2 = √2.</p>
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<p>Simplify the radicals: √8 = 2√2 and √18 = 3√2. Subtract: 3√2 - 2√2 = √2.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>Subtract √27 from 3√12</p>
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<p>Subtract √27 from 3√12</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>Simplify the radicals: √27 = 3√3 and √12 = 2√3. Subtract: 3(2√3) - 3√3 = 3√3.</p>
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<p>Simplify the radicals: √27 = 3√3 and √12 = 2√3. Subtract: 3(2√3) - 3√3 = 3√3.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>Subtract √45 from 2√20</p>
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<p>Subtract √45 from 2√20</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>Simplify the radicals: √45 = 3√5 and √20 = 2√5. Subtract: 2(2√5) - 3√5 = √5.</p>
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<p>Simplify the radicals: √45 = 3√5 and √20 = 2√5. Subtract: 2(2√5) - 3√5 = √5.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>Subtract √32 from √50</p>
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<p>Subtract √32 from √50</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>Simplify the radicals: √32 = 4√2 and √50 = 5√2. Subtract: 5√2 - 4√2 = √2.</p>
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<p>Simplify the radicals: √32 = 4√2 and √50 = 5√2. Subtract: 5√2 - 4√2 = √2.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>Subtract 3√72 from 2√128</p>
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<p>Subtract 3√72 from 2√128</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>No, only like terms with the same radicals can be combined using subtraction; unlike terms must be simplified individually.</h2>
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<h2>No, only like terms with the same radicals can be combined using subtraction; unlike terms must be simplified individually.</h2>
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<h3>1.Is subtraction of irrational numbers commutative?</h3>
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<h3>1.Is subtraction of irrational numbers commutative?</h3>
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<p>No, the subtraction of irrational numbers is not commutative; changing the order changes the outcome.</p>
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<p>No, the subtraction of irrational numbers is not commutative; changing the order changes the outcome.</p>
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<h3>2.What are like terms in the context of irrational numbers?</h3>
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<h3>2.What are like terms in the context of irrational numbers?</h3>
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<p>Like terms have the same radical part. For example, 2√3 and 5√3 are like terms because they share the radical √3.</p>
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<p>Like terms have the same radical part. For example, 2√3 and 5√3 are like terms because they share the radical √3.</p>
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<h3>3.What is the first step in subtracting irrational numbers?</h3>
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<h3>3.What is the first step in subtracting irrational numbers?</h3>
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<p>The first step is to simplify the radicals in each number to identify any like terms for subtraction.</p>
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<p>The first step is to simplify the radicals in each number to identify any like terms for subtraction.</p>
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<h3>4.What method can be used to approximate subtraction of irrational numbers?</h3>
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<h3>4.What method can be used to approximate subtraction of irrational numbers?</h3>
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<p>The decimal approximation method can be used, especially in cases where precision is not crucial.</p>
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<p>The decimal approximation method can be used, especially in cases where precision is not crucial.</p>
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<h2>Common Mistakes and How to Avoid Them in Subtraction of Irrational Numbers</h2>
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<h2>Common Mistakes and How to Avoid Them in Subtraction of Irrational Numbers</h2>
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<p>Subtracting irrational numbers can be tricky and often leads to common errors. Being aware of these mistakes can help avoid them.</p>
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<p>Subtracting irrational numbers can be tricky and often leads to common errors. Being aware of these mistakes can help avoid them.</p>
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<p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>
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<h2>Hiralee Lalitkumar Makwana</h2>
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<h2>Hiralee Lalitkumar Makwana</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.</p>
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<p>Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: She loves to read number jokes and games.</p>
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<p>: She loves to read number jokes and games.</p>