Which is equal to $4 \sqrt{9}+14 \sqrt{4}$?
Answer (1)
Evaluate the square roots: 9 = 3 and 4 = 2 .
Substitute the values into the expression: 4 ( 3 ) + 14 ( 2 ) .
Perform the multiplications: 12 + 28 .
Perform the addition: 12 + 28 = 40 . The final answer is 40 .
Explanation
Understanding the Problem We are asked to find the value of the expression 4 9 + 14 4 .
Evaluating Square Roots First, we need to evaluate the square roots. We know that 9 = 3 because 3 × 3 = 9 , and 4 = 2 because 2 × 2 = 4 .
Substituting Values Now, we substitute these values back into the original expression: 4 ( 3 ) + 14 ( 2 ) .
Performing Multiplications Next, we perform the multiplications: 4 × 3 = 12 and 14 × 2 = 28 . So the expression becomes 12 + 28 .
Performing Addition Finally, we perform the addition: 12 + 28 = 40 . Therefore, the value of the expression 4 9 + 14 4 is 40.
Examples
Understanding how to simplify expressions with square roots is useful in many areas, such as physics and engineering. For example, when calculating the length of the diagonal of a square or the speed of an object in motion, you often encounter square roots. Simplifying these expressions makes the calculations easier and more accurate. Imagine you are building a square garden and need to calculate the length of a diagonal support beam. By simplifying the square root expressions, you can quickly determine the required length.
