Problem 53 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. Check the results by squaring the answer. (Lesson 9.1) $$ \sqrt{64} $$

Step-by-Step Solution

Answer

The square root of 64 is 8.

Step 1: Identify the Square Root

Remember that the square root of a number is a value that, when multiplied by itself, gives the original number. In this case, a number multiplied by itself should give 64.

Step 2: Calculate the Square Root

The number that meets this criteria is 8, since \(8 \times 8 = 64\). So the square root of 64 is 8.

Step 3: Check the Result

To verify that 8 is indeed the square root of 64, square 8 and make sure it results in 64. \(8^2 = 64\), so the answer they got was correct.

Key Concepts

Evaluating Expressions

Evaluating expressions often involves finding the value of specific mathematical terms or symbols. When dealing with square roots, we need to identify the number that when squared (multiplied by itself) gives the original number. In the exercise, we are tasked to find the square root of 64.

To solve this, we look for a number which when squared equals 64. We can start by guessing numbers and squaring them until we find the right one. However, knowing square numbers by heart can be a huge time-saver here. For 64, we know that 8 times 8 equals 64. Therefore, the square root of 64 evaluates to 8.

Square Numbers

Square numbers are simply the result of multiplying a number by itself. These numbers are important because they pop up frequently when dealing with concepts like area, exponents, and particularly when finding square roots. A quick list of some basic square numbers include:

• 1 (since 1 × 1 = 1)
• 4 (since 2 × 2 = 4)
• 9 (since 3 × 3 = 9)
• 16 (since 4 × 4 = 16)
• 25 (since 5 × 5 = 25)
• 64 (since 8 × 8 = 64)

Recognizing these numbers can greatly speed up solving expressions that involve square roots. As we saw in the evaluation of the square root of 64, knowing that 8 is a square number effortlessly leads us to the correct solution.

Verification of Solutions

Verifying a solution in math ensures that the answer obtained is indeed correct. This is especially crucial when working with square roots to double-check our work. Verification involves squaring the number we believe to be the correct square root and checking if it returns the original number.

In our case, since we found that the square root of 64 is 8, we perform a check by calculating \(8^2\). Compute this by multiplying 8 by itself which yields 64. Seeing that \(8 \times 8 = 64\), confirms without a doubt that our solution is correct.

Regular verification not only prevents mistakes but also reinforces confidence in understanding square numbers and their roots. It fosters good habits in math practices that carry over into more complex problems.