Simplify.
StartFraction 5 StartRoot 18 EndRoot minus 2 StartRoot 50 EndRoot over StartRoot 50 EndRoot EndFraction
Answer options with 5 options
A.
1
B.
9 StartRoot 2 EndRoot
C.
15 StartRoot 2 EndRoot minus 2
D.
5 StartRoot 2 EndRoot
E.
3 minus 10 StartRoot 5 EndRoot
To simplify the expression, we can rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator, which is StartRoot 50 EndRoot plus 2.
StartFraction 5 StartRoot 18 EndRoot minus 2 StartRoot 50 EndRoot over StartRoot 50 EndRoot EndFraction
= (5 StartRoot 18 EndRoot minus 2 StartRoot 50 EndRoot) / (StartRoot 50 EndRoot)
= (5 StartRoot 18 EndRoot minus 2 StartRoot 50 EndRoot) / (StartRoot 50 EndRoot) * (StartRoot 50 EndRoot plus 2) / (StartRoot 50 EndRoot plus 2)
= (5 StartRoot 18 EndRoot minus 2 StartRoot 50 EndRoot) (StartRoot 50 EndRoot plus 2) / (StartRoot 50 EndRoot)(StartRoot 50 EndRoot plus 2)
= (5 StartRoot 18*50 EndRoot plus 10 minus 2 StartRoot 50*50 EndRoot minus 4) / (50 + 2 StartRoot 50 EndRoot)
= (5 StartRoot 900 EndRoot plus 10 minus 2 StartRoot 2500 EndRoot minus 4) / (50 + 2 StartRoot 50 EndRoot)
= (5 * 30 plus 10 minus 2 * 50 minus 4) / (50 + 2 StartRoot 50 EndRoot)
= (150 + 10 - 100 - 4) / (50 + 2 StartRoot 50 EndRoot)
= 56 / (50 + 2 StartRoot 50 EndRoot)
= 28/25 + StartRoot 2 EndRoot / (25 + StartRoot 2 EndRoot)
Therefore, the simplified expression is 28/25 + StartRoot 2 EndRoot / (25 + StartRoot 2 EndRoot).
None of the given answer options match the simplified expression.