Question

What is \(\sqrt{36}\) ? Write your answer in the box.

Short answer

The square root of 36 is 6.

Step-by-step solution

Understand the Problem

The problem asks for the value of the square root of 36. The square root of a number is a value that, when multiplied by itself, gives the original number.

Recall the Definition of Square Root

By definition, \(\text{if } x = \sqrt{36}, \text{ then } x^2 = 36\).

Find the Value

Identify a number \(x\) that, when squared, equals 36. Since \(6 \times 6 = 36\), \(\text{we have found that } \sqrt{36} = 6\).

Verify the Solution

Check the result by squaring it: \(6^2 = 36\), which confirms that the solution is correct.

Key concepts

Square Root Definition

The square root of a number is a value which, when multiplied by itself, results in the original number. In mathematical symbols, if \( x = \sqrt{a} \), then \( x^2 = a \). For example: \( \sqrt{36} \) is 6 because 6 multiplied by 6 is 36. Understanding this concept is crucial for solving problems involving square roots.
You might come across both positive and negative square roots because both positive and negative values, when squared, give the original number: \(6^2 = 36 \) and \((-6)^2 = 36 \). However, by convention, when we refer to the square root symbol \( \sqrt{} \), we usually mean the positive square root.
This makes identification and verification of solutions simpler and more intuitive.

Verifying Solutions

Verifying your solution means confirming that the answer you found is correct. In the context of square roots, verification involves squaring the result to see if it matches the original number.
For the given problem, we claimed that \( \sqrt{36} = 6 \). To verify:

• Square the solution: \( 6^2 = 36 \).
• Since the original problem was to find the square root of 36, and squaring our solution 6 indeed gives 36, the solution is verified to be correct.

This step is critical, as it gives confidence that the solution is accurate and reliable.
Verification helps identify any possible mistakes in calculation or understanding and is a good habit, not just in algebra but in all mathematical problems.

Basic Algebra

Basic algebra involves foundational mathematical concepts that include operations with numbers, solving equations, and understanding properties of numbers. In this exercise:

• We used the concept of exponents. When we say \( x^2 \), it means multiplying x by itself.
• We solved for \( x \) by finding a number that satisfies the equation \( x^2 = 36 \).

These basics are essential for understanding more complex algebraic expressions and functions.
In algebra, knowing the properties and definitions such as that of square roots, is vital because it simplifies solving equations and parsing through problems. The more familiar you are with algebraic rules and concepts, the more efficiently you can approach and solve mathematical problems of increasing complexity.
Think of basic algebra as the building blocks for your math skills. Mastering these concepts will provide a strong foundation for advanced study in mathematics.