The expression 10 - √18 / √2 simplifies to 7 when rationalizing the denominator and simplifying. The form a + b√2 results in a = 7 and b = 0.
The student is asking how to simplify the expression 10 - √18 / √2 and express it in the form of a + b√2, where a and b are integers.
To solve this, we need to rationalize the denominator and simplify the expression.
First, we simplify √18 by recognizing it as √(9×2) which is √9 × √2, hence 3√2.
This gives us the expression 10 - 3√2 / √2.
Dividing 3√2 by √2 gives us 3.
Therefore, the expression simplifies to 10 - 3, which equals 7. Thus, a equals 7 and b equals 0.
The student's initial query can be answered with a = 7 and b = 0.