Questions: Find the value of the indicated expression. 3 sqrt(16)-4 sqrt(4)

Find the value of the indicated expression. 3 sqrt(16)-4 sqrt(4)
Transcript text: Find the value of the indicated expression. \[ 3 \sqrt{16}-4 \sqrt{4} \]
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Solution

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Solution Steps

To solve the given expression, we need to evaluate the square roots and then perform the arithmetic operations. Specifically, we will:

  1. Calculate the square root of 16.
  2. Calculate the square root of 4.
  3. Multiply the results by their respective coefficients.
  4. Subtract the second product from the first.
Step 1: Calculate the Square Roots

We start by calculating the square roots of the numbers in the expression: \[ \sqrt{16} = 4 \] \[ \sqrt{4} = 2 \]

Step 2: Multiply by Coefficients

Next, we multiply each square root by its respective coefficient: \[ 3 \cdot \sqrt{16} = 3 \cdot 4 = 12 \] \[ 4 \cdot \sqrt{4} = 4 \cdot 2 = 8 \]

Step 3: Perform the Subtraction

Now, we subtract the second product from the first: \[ 3 \sqrt{16} - 4 \sqrt{4} = 12 - 8 = 4 \]

Final Answer

The value of the indicated expression is \(\boxed{4}\).

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