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If a=0.1125, then find the value of 100[1+2(3a)+9a2тАЛтИТ4a].
85.57
88.75
87.75
87.57
88.75
Recognize the identity (1 + 3a)2 = 1 + 6a + 9a┬▓ inside the square root to simplify the expression to 100(1 - a) immediately.
The value of a = 0.1125, and the expression to evaluate is 100[sqrt(1 + 2(3a) + 9a┬▓) - 4a].
100[(1+3a)2тАЛтИТ4a]
Recognize the identity (1 + 3a)2 = 1 + 6a + 9a┬▓ inside the square root to simplify the expression to 100(1 - a) immediately.
Students often struggle to simplify the square root of (1+3a)2 correctly, sometimes ignoring the negative sign or miscalculating the final subtraction.
Simplify the expression inside the square root
Recognize that the term inside the square root is a perfect square: 1+2(3a)+9a2=1+6a+(3a)2=(1+3a)2.
1+2(3a)+9a2тАЛ=(1+3a)2тАЛ=1+3a
Substitute back into the main equation
Substitute the simplified root into the original expression: 100[(1+3a)тИТ4a]=100[1тИТa].
100(1тИТa)
Evaluate with the given value of a
Given a=0.1125, calculate 100(1тИТ0.1125)=100(0.8875).
100├Ч0.8875=88.75
B is correct because the expression simplifies to 100(1 - a), which equals 100(0.8875) = 88.75.
Always look for perfect square binomial expansions (x+y)2 when you see a radical term containing squared variables in competitive exams.
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