- √5 + √3
- 2√2 + 2√6
- 2√5 + 2√3
- √2 + √6

Option 1 : √5 + √3

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**Formula used:**

(a + b)^{2} = a^{2} + b^{2} + 2ab

**Calculation:**

Given expression is:

\(\sqrt {8\; + \;2\sqrt {15} \;} \)

= \(\sqrt {5\; + \;3\; + \;2\sqrt 5 \sqrt 3 \;}\)

= \(\sqrt {{{(\sqrt 5 )}^2}\; + \;{{\left( {\sqrt 3 } \right)}^2}\; + \;2\sqrt 5 \sqrt 3 \;} \)

= \(\sqrt {{{\left( {\;\sqrt 5 \; + \;\sqrt 3 \;} \right)}^2}\;}\)

= \(\sqrt 5 + \sqrt 3\)

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