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13 Mar 2020, 02:59
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
54% (02:03) correct
46%
(02:10)
wrong
based on 296
sessions
History
Date
Time
Result
Not Attempted Yet
\(x\) denotes the decimal fraction part of \(\sqrt{57}\). What is \(x(x + 14)\)?
A. \(6\)
B. \(7\)
C. \(8\)
D. \(9\)
E. \(10\)
A. \(6\)
B. \(7\)
C. \(8\)
D. \(9\)
E. \(10\)
13 Mar 2020, 03:40
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7^2<57<8^2
\(\sqrt{57}= 7.abc\)
\(\sqrt{57}= 7+x\)
Squaring both sides
57= x^2+14x+49
x^2+14x= 8
x(x+14) =8
\(\sqrt{57}= 7.abc\)
\(\sqrt{57}= 7+x\)
Squaring both sides
57= x^2+14x+49
x^2+14x= 8
x(x+14) =8
MathRevolution
General Discussion
16 Mar 2020, 04:06
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=>
\(7 = √49 < √57 < √64 = 8\)
We have \(x = √57 – 7\) since \(x\) denotes the decimal fraction part of \(\sqrt{57}.\)
Then
\(x(x + 14) = (√57 – 7)(√57 + 14 - 7) \)
\(x(x + 14) = (√57 – 7)(√57 + 7) \) (adding like terms)
\(x(x + 14) = 57 + 7√57 - 7√57 – 49\) (foiling the right side)
\(x(x + 14) = 57 – 49\) (cancelling terms)
\(x(x + 14) = 8\) (adding like terms)
Therefore, C is the answer.
Answer: C
\(7 = √49 < √57 < √64 = 8\)
We have \(x = √57 – 7\) since \(x\) denotes the decimal fraction part of \(\sqrt{57}.\)
Then
\(x(x + 14) = (√57 – 7)(√57 + 14 - 7) \)
\(x(x + 14) = (√57 – 7)(√57 + 7) \) (adding like terms)
\(x(x + 14) = 57 + 7√57 - 7√57 – 49\) (foiling the right side)
\(x(x + 14) = 57 – 49\) (cancelling terms)
\(x(x + 14) = 8\) (adding like terms)
Therefore, C is the answer.
Answer: C
