Problem 291 - Intermediate Algebra

Question

In the following exercises, simplify. $$ \sqrt{64} $$

Step-by-Step Solution

Answer

The simplified form of \( \sqrt{64} \) is 8.

Step 1: Identify the radicand

The radicand is the number inside the square root symbol. Here, the radicand is 64.

Step 2: Determine the square root

Find which number multiplied by itself gives the radicand 64. We need to determine the number that when squared results in 64.

Step 3: Calculate the square root

The number that multiplied by itself equals 64 is 8. This is because: \[8 \times 8 = 64\]

Key Concepts

Radicand

The radicand is a fundamental concept in square root calculations. It is the number located inside the square root symbol (√). For instance, in the problem \( \sqrt{64} \) , the number 64 is the radicand. Understanding this helps you identify the number you need to consider when simplifying square roots.

Square Root Calculation

To simplify a square root, you must find a number that, when multiplied by itself, equals the radicand. This number is called the square root. For example, to simplify \( \sqrt{64} \) , we look for a number that, when squared, equals 64. Here's the step-by-step process:

• First, identify the radicand (64 in this case).
• Next, determine which number, when multiplied by itself, equals 64.
• The number 8 fulfills this requirement because \( 8 \times 8 = 64 \). Therefore, \( 8 \) is the square root of 64.

Mathematical Steps

Following a clear process can make simplifying square roots straightforward. Here’s how you do it with our example \( \sqrt{64} \):

• Step 1: Identify the Radicand
  The first step is to determine what number is inside the square root symbol. For \( \sqrt{64} \) , the radicand is 64.
• Step 2: Determine the Square Root
  The next step is to find out which number, when squared, gives 64. This involves thinking of multiplication pairs that result in 64.
• Step 3: Calculate the Square Root
  The final step is to verify that 8 is the square root, as 8 \( \times 8 \) equals 64. So, \( \sqrt{64} = 8 \) is the simplified form.

Following these mathematical steps ensures that you can simplify any square root correctly.