Check if the number is a perfect square

Oct 13, 2025 by vinooalluri.com 139 views

Introduction

When evaluating the square root of a number, we are looking for a value that, when multiplied by itself, gives us the original number. In this case, we are given the task of finding the square root of 289. We will show our work step by step to arrive at the final answer.

Understanding Square Roots

A square root of a number is a value that, when multiplied by itself, gives us the original number. For example, the square root of 16 is 4, because 4 multiplied by 4 equals 16. Similarly, the square root of 25 is 5, because 5 multiplied by 5 equals 25.

Evaluating the Square Root of 289

To evaluate the square root of 289, we need to find a value that, when multiplied by itself, gives us 289. We can start by looking for perfect squares that are less than or equal to 289. A perfect square is a number that can be expressed as the product of an integer with itself.

Perfect Squares Less Than or Equal to 289

Some perfect squares less than or equal to 289 are:

1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
9^2 = 81
10^2 = 100
11^2 = 121
12^2 = 144
13^2 = 169
14^2 = 196
15^2 = 225
16^2 = 256
17^2 = 289

Finding the Square Root of 289

As we can see from the list above, 17^2 equals 289. Therefore, the square root of 289 is 17.

Conclusion

In this article, we evaluated the square root of 289 by looking for perfect squares that are less than or equal to 289. We found that 17^2 equals 289, and therefore, the square root of 289 is 17.

Frequently Asked Questions

Q: What is the square root of 289?

A: The square root of 289 is 17.

Q: How do I evaluate the square root of a number?

A: To evaluate the square root of a number, you need to find a value that, when multiplied by itself, gives us the original number. You can start by looking for perfect squares that are less than or equal to the number.

Q: What is a perfect square?

A: A perfect square is a number that can be expressed as the product of an integer with itself.

Final Answer

The final answer is: $\boxed{17}$

Introduction

Evaluating square roots is an essential skill in mathematics, and it's used in various fields such as algebra, geometry, and trigonometry. In this article, we will provide a comprehensive guide on how to evaluate square roots, including tips and tricks to make it easier.

Understanding Square Roots

Evaluating Square Roots: A Step-by-Step Guide

To evaluate the square root of a number, follow these steps:

Look for perfect squares: Start by looking for perfect squares that are less than or equal to the number. A perfect square is a number that can be expressed as the product of an integer with itself.
Check if the number is a perfect square: If the number is a perfect square, then its square root is the integer that was multiplied by itself to get the perfect square.
Use the square root symbol: If the number is not a perfect square, then its square root is an irrational number. In this case, we can use the square root symbol (√) to represent the square root of the number.
Simplify the expression: If the expression contains a square root, we can simplify it by multiplying the square root by itself.

Tips and Tricks for Evaluating Square Roots

Here are some tips and tricks to make evaluating square roots easier:

Use a calculator: If you're having trouble evaluating a square root, you can use a calculator to find the approximate value.
Look for patterns: Look for patterns in the numbers to help you evaluate the square root.
Use the square root formula: If you're dealing with a square root of a fraction, you can use the square root formula: √(a/b) = √a / √b.
Simplify the expression: If the expression contains a square root, simplify it by multiplying the square root by itself.

Frequently Asked Questions

Q: What is the square root of 289?

A: The square root of 289 is 17.

Q: How do I evaluate the square root of a number?

Q: What is a perfect square?

A: A perfect square is a number that can be expressed as the product of an integer with itself.

Q: How do I simplify an expression with a square root?

A: To simplify an expression with a square root, multiply the square root by itself.

Q: What is the square root of a fraction?

A: The square root of a fraction is the square root of the numerator divided by the square root of the denominator.

Q: How do I use a calculator to evaluate a square root?

A: To use a calculator to evaluate a square root, enter the number and press the square root button.

Common Mistakes to Avoid

Here are some common mistakes to avoid when evaluating square roots:

Not looking for perfect squares: Make sure to look for perfect squares that are less than or equal to the number.
Not simplifying the expression: Make sure to simplify the expression by multiplying the square root by itself.
Not using the square root formula: Make sure to use the square root formula when dealing with a square root of a fraction.

Conclusion

Evaluating square roots is an essential skill in mathematics, and it's used in various fields such as algebra, geometry, and trigonometry. By following the steps outlined in this article, you can evaluate square roots with ease. Remember to look for perfect squares, simplify the expression, and use the square root formula when dealing with a square root of a fraction.

Final Answer

The final answer is: $\boxed{17}$