What is the true statement about the sum of the square root of 50 and the square root of 18?

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To analyze the sum of the square roots of 50 and 18, let’s break down the calculation step-by-step:

Step 1: Calculate square roots

First, we need to determine the square roots:

  • Square root of 50: This can be simplified. The square root of 50 is the same as the square root of 25 times the square root of 2. Therefore, we have:
    • √50 = √(25 × 2) = √25 × √2 = 5√2
  • Square root of 18: Similarly, we can simplify the square root of 18:
    • √18 = √(9 × 2) = √9 × √2 = 3√2

Step 2: Sum the square roots

Now, we will add the two results:

Sum = √50 + √18 = 5√2 + 3√2

This can be simplified further:

Sum = (5 + 3)√2 = 8√2

Step 3: True statement

Now we can conclude that the sum of the square root of 50 and the square root of 18 is represented as:

8√2

In a numerical approximation, using the fact that √2 is approximately 1.414, we can further calculate:

8√2 ≈ 8 × 1.414 ≈ 11.312

Final Statement

Therefore, the true statement is that the sum of the square root of 50 and the square root of 18 is equal to 8√2, which approximates to about 11.312.

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