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Maths-

General

Easy

Question

Let $open square brackets x close square brackets$ denote the greatest integer less than or equal to $x$ . If $x equals open parentheses square root of 3 plus 1 close parentheses to the power of 5 end exponent$ , then $open square brackets x close square brackets$ is equal to

75
50
76
152

The correct answer is: 152

$x equals open parentheses square root of 3 plus 1 close parentheses to the power of 5 end exponent equals open parentheses square root of 3 close parentheses to the power of 5 end exponent plus blank to the power of 5 end exponent C subscript 1 end subscript open parentheses square root of 3 close parentheses to the power of 4 end exponent plus blank to the power of 5 end exponent C subscript 2 end subscript open parentheses square root of 3 close parentheses to the power of 3 end exponent$
$plus blank to the power of 5 end exponent C subscript 3 end subscript open parentheses square root of 3 close parentheses to the power of 2 end exponent plus blank to the power of 5 end exponent C subscript 4 end subscript left parenthesis square root of 3 right parenthesis end root plus blank to the power of 5 end exponent C subscript 5 end subscript$
$equals 9 square root of 3 plus 45 plus 30 square root of 3 plus 30 plus 5 square root of 3 plus 1$
$equals 76 plus 44 square root of 3$
$therefore blank open square brackets x close square brackets equals open square brackets open parentheses square root of 3 plus 1 close parentheses to the power of 5 end exponent close square brackets equals open square brackets 76 plus 44 square root of 3 close square brackets$
$equals open square brackets 76 close square brackets plus open square brackets 44 cross times 1.732 close square brackets$
$equals 76 plus left square bracket 76.2 right square bracket$
$equals 76 plus 76 equals 152$

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