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Combine your skills of working with exponents and manipulating expressions for radical glory.
Evaluate
\[ ( \sqrt{ 12 } - 1 ) ( \sqrt{ 12 } + 1 ). \]
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True or False:
For all real numbers \( a \) and \( b, \)
\[ \left( \sqrt{a} + \sqrt{b} \right) ^2 = a + b .\]
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How many real solutions are there to
\[ x - 4 = 2 \sqrt{ x - 1 } ?\]
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The velocity (V) of an object can be obtained from the kinetic energy (KE) of the object and its mass (M) using the following formula:
\[ V = \sqrt{ \frac{ 2 KE } { M } }. \]
If the new kinetic energy of the object (with the same mass) is 4 times the old kinetic energy, what can we say about the new velocity of the object?
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What is the value of
\[ \sqrt{ 1 + \frac{ 16}{ 9 } } ? \]
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