45+2923=we can solve it by using options3+2If 3+2=45+2923then (3+2)3=45+292we solve and check(3+2)3=27+22+18+272=45+292so,option 1 is correct 45+2923=3+2

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$\sqrt[3]{45 + 29 \sqrt{2}} =$

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$1 + 2 \sqrt{2}$

$3 + \sqrt{2}$

$2 + \sqrt{2}$

$3 + 2 \sqrt{2}$

answer is A.

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Detailed Solution

$\sqrt[3]{45 + 29 \sqrt{2}} =$
we can solve it by using options
$3 + \sqrt{2}$
If $3 + \sqrt{2} = \sqrt[3]{45 + 29 \sqrt{2}}$
then $(3 + \sqrt{2})^{3} = 45 + 29 \sqrt{2}$
we solve and check
$\begin{matrix} (3 + \sqrt{2})^{3} = 27 + 2 \sqrt{2} + 18 + 27 \sqrt{2} \\ = 45 + 29 \sqrt{2} \end{matrix}$
so,option 1 is correct $\sqrt[3]{45 + 29 \sqrt{2}} = 3 + \sqrt{2}$