Question

tell this to be brainliest please
$\sqrt{7 + 2 \sqrt{10 } } = what$

Answer 1

Whatever the number comes by solving the above one is always be a irrational number.
Answer is
3.6496...................

Answer 2

$\sqrt{7 + 2 \sqrt{10} } = \sqrt{x} + \sqrt{y} \\ squaring \: both \: sides \\ 7 + 2 \sqrt{10} = x + y + 2 \sqrt{xy} \\ comparing \: both \: sides \\ x + y = 7 \\ xy = 10 \\ y = \frac{10}{x} \\ x + \frac{10}{x} = 7\\ {x}^{2} + 10 = 7x \\ {x}^{2} - 7x + 10 = 0 \\solve \:it \:by\: factorisation\: a\: method \\x= 5 \\ put \: into \: x + y = 7 \\ x = 5 \\ hence \: y = 2 \\ so \: \sqrt{7 + 2 \sqrt{10} } = \sqrt{5} + \sqrt{2}$
Or you can directly observe that
$\sqrt{5 + 2 + 2 \sqrt{5 \times 2} } \\ it \: is \: becoming \: \\ \sqrt{ {( \sqrt{5} + \sqrt{2} )}^{2} } = \sqrt{5 } + \sqrt{2}$

Hope this helps you.....