Which statement is true about the product square root of 2 (3square root of 2 + square root of 18 )

To determine if the statement about the product is true, we need to simplify and calculate the product given by the square root of 2 multiplied by the expression (3 square root of 2 + square root of 18). Let's perform these calculations step by step

Step 1: First, simplify the square root of 18. Since 18 can be broken down into 9 × 2, and since the square root of 9 is 3, the square root of 18 is the square root of 9 multiplied by the square root of 2, which gives us 3 square root of 2.

Step 2: Now, we have the expression in a simpler form: square root of 2 (3 square root of 2 + 3 square root of 2).

Step 3: Combine like terms in the parentheses: 3 square root of 2 + 3 square root of 2 equals 6 square root of 2.

Step 4: Multiply the square root of 2 outside of the parentheses by the expression inside the parentheses (6 square root of 2).

Step 5: When multiplying two square roots with the same radicand (the number inside the square root), the result is the number under the square roots. So, square root of 2 × square root of 2 equals 2.

Step 6: Multiply this result by the 6 outside of the square root to get the final simplified form: 2 × 6 = 12.

Therefore, the initial expression simplifies to 12, and the statement is true only if it asserts that the product is 12.