Final answer:
The expression simplifies to 4√2, after breaking down the square root of 18 into 3√2 and multiplying it by √2, then subtracting the result from 10.
Step-by-step explanation:
The question asks to simplify the expression 10 - √18 × √2 and express it in the form of a × b√2, where 'a' and 'b' are real numbers. To do this, we first simplify √18 by finding the largest square factor of 18, which is 9, and rewriting √18 as √(9×2). We know that √9 is 3, so we can express √18 as 3√2. Next, we multiply 3√2 by √2, which gives us 3×2 because when we multiply square roots of the same number, we get the number itself. This simplifies to 6. Finally, we subtract 6 from 10 to get the simplified form 4, which can be written as 4 × 1√2, so a = 4 and b = 1. Therefore, the expression simplifies to 4√2.