What Is the Square Root of 289

The concept of square root of 289 plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios.

What Is Square Root of 289?

A square root of 289 is defined as the number which, when multiplied by itself, gives 289. In mathematical terms, \( \sqrt{289} = 17 \) because \( 17 \times 17 = 289 \). You’ll find this concept applied in topics such as perfect squares, area calculation, and solving quadratic equations.

Key Formula for Square Root of 289

Here’s the standard formula: \( \sqrt{289} = 17 \)

Cross-Disciplinary Usage

Square root of 289 is not only useful in Maths but also plays an important role in Physics, Computer Science, and daily logical reasoning. Students preparing for JEE or NEET will see its relevance in geometry, algebra, and data analysis questions.

Step-by-Step Illustration

1. Start with the question: What is \( \sqrt{289} \)?
   
   Since 289 is a perfect square, find which number squared gives 289.
2. Prime Factorization Method:
   
   1. Write 289 as 17 × 17 (since 17 is a prime number).
   2. Now, \( \sqrt{17 \times 17} = 17 \).
3. Long Division Method:
   
   1. Group 289 as “2” and “89”.
   2. 4 × 4 = 16 (try 1 digit). Next, bring down 89.
   3. Through steps, you reach 17 as the answer.
4. Final Answer:
   
   The square root of 289 is 17.

Speed Trick or Vedic Shortcut

Here’s a quick shortcut that helps solve problems faster when working with square root of 289. Many students use this trick during timed exams to save crucial seconds.

Example Trick: If you know 289 ends with 9 and is near 16² (256) and 17² (289), guess which integer square is closest. Since 17 × 17 = 289, the answer is 17.

1. Recognize that perfect squares from 10² (100) to 20² (400) are easy to memorize for exams.
2. Spot the last two digits: 89 in 289 match the second digit pattern of some common squares (e.g., 17² = 289).
3. Try squaring 17 quickly: \( 17 \times 17 = 17 \times (10 + 7) = 170 + 119 = 289 \).
4. Final Answer: 17 is the square root of 289.

Tricks like this aren’t just cool — they’re practical in competitive exams like NTSE, Olympiads, and even JEE. Vedantu’s live sessions include more such shortcuts to help you build speed and accuracy.

Try These Yourself

• Find the square root of 28900.
• Check if 361 is a perfect square like 289.
• Find all perfect square numbers between 250 and 300.
• Solve: What is the square root of 225?

Frequent Errors and Misunderstandings

• Confusing square root of 289 (\( \sqrt{289} \)) with “half of 289.”
• Assuming 289 is not a perfect square due to last digit pattern.
• Skipping stepwise calculation and making errors in long division.

Relation to Other Concepts

The idea of square root of 289 connects closely with topics such as Square Root of 169 and Square Root of 225. Mastering this helps with understanding more advanced concepts in algebra and geometry.

Classroom Tip

A quick way to remember the square root of 289 is that it matches 17 squared: 17 × 17 = 289. Vedantu’s teachers often use this multiplication trick as a visual cues chart for perfect squares up to 20 × 20 during live classes for rapid recall.

Wrapping It All Up

We explored square root of 289—from definition, formula, examples, mistakes, and connections to other subjects. Continue practicing with Vedantu to become confident in solving problems using this concept.

More Practice and Related Topics

• Square Root of 169
• Square Root of 225
• Square Root by Division Method
• Prime Factorization Method
• Square Root Calculator