# Let #sqrt(1 + sqrt(3 + sqrt(5+ sqrt(x)))) = 2# What x?

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To find the value of ( x ), we first square both sides of the equation ( \sqrt{1 + \sqrt{3 + \sqrt{5 + \sqrt{x}}}} = 2 ). This yields:

[ 1 + \sqrt{3 + \sqrt{5 + \sqrt{x}}} = 4 ]

Next, we subtract 1 from both sides:

[ \sqrt{3 + \sqrt{5 + \sqrt{x}}} = 3 ]

We square both sides again:

[ 3 + \sqrt{5 + \sqrt{x}} = 9 ]

Then, subtract 3 from both sides:

[ \sqrt{5 + \sqrt{x}} = 6 ]

Square both sides again:

[ 5 + \sqrt{x} = 36 ]

Subtract 5 from both sides:

[ \sqrt{x} = 31 ]

Square both sides one more time:

[ x = 961 ]

So, ( x = 961 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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