GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
If p = \sqrt3 -2/\sqrt2 + 1, then which of the following
[#permalink]
16 Apr 2019, 01:26
16 Apr 2019, 01:26
Expert Reply
00:00
Question Stats:
57% (01:01) correct
42% (01:39) wrong based on 7 sessions
Hide Show timer Statistics
If \(p = \frac{\sqrt{3} -2}{\sqrt{2} + 1}\), then which of the following equals \(p-4\) ?
A. \(\sqrt{3} - 2\)
B. \(\sqrt{3} + 2\)
C. \(2\)
D. \(-2 \sqrt{2} + \sqrt{6} - \sqrt{3} - 2\)
E. \(- 2 \sqrt{2} + \sqrt{6} - \sqrt{3} + 2\)
A. \(\sqrt{3} - 2\)
B. \(\sqrt{3} + 2\)
C. \(2\)
D. \(-2 \sqrt{2} + \sqrt{6} - \sqrt{3} - 2\)
E. \(- 2 \sqrt{2} + \sqrt{6} - \sqrt{3} + 2\)
Re: If p = \sqrt3 -2/\sqrt2 + 1, then which of the following
[#permalink]
09 Nov 2019, 15:59
09 Nov 2019, 15:59
any explanation on this one algebraically? can do it via calculator easily but not the point...
Re: If p = \sqrt3 -2/\sqrt2 + 1, then which of the following
[#permalink]
09 Nov 2019, 19:05
09 Nov 2019, 19:05
1
Expert Reply
The question is easy if you do know the exponent rule of rationalization
\(p= \frac{\sqrt{3} - 2 }{\sqrt{2} + 1 }\) \(= \frac{\sqrt{3} - 2}{\sqrt{2} + 1} \times \frac{\sqrt{2} - 1}{\sqrt{2} -1} =\) \(\frac{\sqrt{3} \sqrt{2} + \sqrt{3} -1 + -2 \sqrt{2} + -2-1}{(\sqrt{2})^2 -1^2}\)
Do the calculation
\(p-4=\sqrt{6} - \sqrt{3}-2 \sqrt{2} + 2= \sqrt{6} - \sqrt{3} -2 \sqrt{2} -2 = D\)
\(p= \frac{\sqrt{3} - 2 }{\sqrt{2} + 1 }\) \(= \frac{\sqrt{3} - 2}{\sqrt{2} + 1} \times \frac{\sqrt{2} - 1}{\sqrt{2} -1} =\) \(\frac{\sqrt{3} \sqrt{2} + \sqrt{3} -1 + -2 \sqrt{2} + -2-1}{(\sqrt{2})^2 -1^2}\)
Do the calculation
\(p-4=\sqrt{6} - \sqrt{3}-2 \sqrt{2} + 2= \sqrt{6} - \sqrt{3} -2 \sqrt{2} -2 = D\)
