MCQ
$\sqrt[3]{{(61 - 46\sqrt 5 )}} = $
- ✓$1 - 2\sqrt 5 $
- B$1 - \sqrt 5 $
- C$2 - \sqrt 5 $
- DNone of these
✓
Answer
Correct option: A.
$1 - 2\sqrt 5 $
a
(a) $\sqrt[3]{{61 - 46\sqrt 5 }} = a - \sqrt b $
(a) $\sqrt[3]{{61 - 46\sqrt 5 }} = a - \sqrt b $
==> $61 - 46\sqrt 5 = {(a - \sqrt b )^3} = {a^3} + 3ab - (3{a^2} + b)\sqrt b $
==> $61 = {a^3} + 3ab,\,46\sqrt 5 = (3{a^2} + b)\,\sqrt b $
==> $61 = ({a^2} + 3b)\,a$, $23\sqrt {20} = (3{a^2} + b)\sqrt b $
So,$a = 1,\,\,b = 20$.
Therefore, $\sqrt[3]{{61 - 46\sqrt 5 }} = 1 - \sqrt {20} = 1 - 2\sqrt 5 $.
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