Simplify.

Question

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

Answer 1

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.