Question

the square root of 11+√112 is​

Answer 1

√(11+√112 )

4.65

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Answer 2

Answer:

The answer is √7 + 2

Step-by-step explanation:

Here, the given expression is,

$11 + \sqrt{112}$,

$= 11 + \sqrt{4\times 28}$

$= 11 + \sqrt{4} \times \sqrt{28}$

$= 11 + 2 \times \sqrt{28}$

$= 11 + 2 \times \sqrt{7} \times \sqrt{4}$

$= 7 + 4 + 2 \times \sqrt{7} \times \sqrt{4}$

$= (\sqrt{7})^2 + (\sqrt{4})^2 + 2\times \sqrt{7}\times \sqrt{4}$

$= (\sqrt{7} + \sqrt{4})^2$

Thus, 11 + √112 = (√7 + √4)²

Hence,

$\sqrt{11+\sqrt{112}}=\sqrt{(\sqrt{7}+\sqrt{4})^2}=\sqrt{7}+\sqrt{4}=\sqrt{7}+2$