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Sub 505 (Easy)|   Algebra|   Roots|      
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Bunuel
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If (1 + (1 + x^(1/2)^(1/2))^(1/2) = 2, then x = 15 Aug 2023, 12:00
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91% (01:07) correct 9% (01:29) wrong based on 580 sessions

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If \(\sqrt{1 + \sqrt{1 +\sqrt{ x} } } = 2\), then x =

A. 2
B. 8
C. 9
D. 64
E. 81

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D
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If (1 + (1 + x^(1/2)^(1/2))^(1/2) = 2, then x = 15 Aug 2023, 13:22
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Bunuel
If \(\sqrt{1 + \sqrt{1 +\sqrt{ x} } } = 2\), then x =

A. 2
B. 8
C. 9
D. 64
E. 81
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\(\sqrt{1 + \sqrt{1 +\sqrt{ x} } } = 2\)

Squaring both sides of the equation

\(1 + \sqrt{1 +\sqrt{ x} } = 4\)

\( \sqrt{1 +\sqrt{ x} } = 3\)

Squaring both sides of the equation

\( 1 +\sqrt{ x} = 9\)

\( \sqrt{ x} = 8\)

Squaring both sides of the equation

\( x = 64\)

Option D
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If (1 + (1 + x^(1/2)^(1/2))^(1/2) = 2, then x = 06 Apr 2025, 07:06
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Could someone explain this to me?
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If (1 + (1 + x^(1/2)^(1/2))^(1/2) = 2, then x = 06 Apr 2025, 08:44
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Moving to the appropriate sub forum.
You can solve this question in a few ways, the fast and easy one is probably using backsolving.

This is the most reliable method if you are lost about how to solve questions. I get an answer such as a nine or an eight and see what happens. If an answer choice doesn’t work, take a greater or a smaller one. It should not take you more than 30 or 60 seconds to solve it
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If (1 + (1 + x^(1/2)^(1/2))^(1/2) = 2, then x = 06 Apr 2025, 09:28
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(√1+(√1+(√x)))= 2
Squaring both sides
1+(√1+(√x))=4
(√1+(√x))=4-1=3
Again squaring both sides
1+√x= 9
√x=9-1=8
Again squaring both sides
x=64
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If (1 + (1 + x^(1/2)^(1/2))^(1/2) = 2, then x = 06 Apr 2025, 10:05
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Merged the topic to an existing discussion.
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