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Expansion of (a + b)^2

The value of ...

Question

The value of $\sqrt{5 + \sqrt{11 + \sqrt{19 + \sqrt{20 + \sqrt{49}}}}}$ on simplifying is

A

1

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B

2

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C

4

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D

3

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Solution

The correct option is D 3
Consider, $\sqrt{5 + \sqrt{11 + \sqrt{19 + \sqrt{20 + \sqrt{49}}}}}$
= $\sqrt{5 + \sqrt{11 \sqrt{19 + \sqrt{20 + 7}}}}$
= $\sqrt{5 + \sqrt{11 + \sqrt{19 + 4.20}}}$
= $\sqrt{5 + \sqrt{11 + \sqrt{23.20}}}$
$= \sqrt{5 + \sqrt{11 + 4.82}} = \sqrt{5 + \sqrt{15.82}}$
$= \sqrt{5 + 3.99} = \sqrt{8.99} = 3$

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Similar questions

Q. The value of

\sqrt{5 + \sqrt{11 + \sqrt{19 + \sqrt{29 + \sqrt{49}}}}}

Simplify: 20 ÷ [19 - {14 - 5}]

Simplify: 20 ÷ [19 - {14 - 5}]

(- 1)^{19} + (- 1)^{20} + (2)^{5}

\frac{7}{11} \times \frac{33}{49} \times \frac{14}{44}

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