Answer:
a=-3, b=5
Explanation:
Given that:
10-√18/√2=a+b√2
We need to find values of a and b.
All we have to do is solve 10-√18/√2
The first step is to simplify √18
√18=√9×2=3√2
The second step is to rationalize the whole fraction, by removing an irrational number as the denominator
10-√18/√2 = 10-3√2/√2 × √2/√2
Distribute √2:
10√2-3×√2²/√2²
10√2-6/2
Factor out 2 from the expression:
2(5√2-3)/2
Cancel out the 2, and the final answer is:
5√2-3
Thus, a=-3 and b=5
Hope this helps!