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Problems based on Numbers Test 2

Question : 1 of 40

Marks: +1, -0

The value of

\sqrt{7-\sqrt{7+\sqrt{7-\sqrt{7-\dots\infty}}}}

is:

Solution:

Concept:

For an infinite nested radical with a repeating pattern, set the whole expression equal to

x

and solve the resulting equation.

Explanation:

Let

x=\sqrt{7-\sqrt{7+\sqrt{7-\sqrt{7+\cdots}}}}

Because the pattern repeats, the part inside

7+

is also

x

So,

x=\sqrt{7-\sqrt{7+x}}

Square both sides:

x^2=7-\sqrt{7+x}

Now test the given options.

For

x=2

x^2=4

7-\sqrt{7+x}=7-\sqrt{9}=7-3=4

Both sides match.

Answer:

The value is

2

(Option B).

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