Question

How to solve it??



Plzzz help me out

Answer 1

$3 \sqrt{147} - 5 \sqrt{ \frac{1}{3} } + 9 \sqrt{ \frac{1}{3} } \\ \\ = 3 \sqrt{49 \times 3} - 5 \sqrt{ \frac{1}{3} } + 9 \sqrt{ \frac{1}{3} } \\ \\ = 3 \times 7 \sqrt{3} - 5 \sqrt{ \frac{1}{3} } + 9 \sqrt{ \frac{1}{3} } \\ \\ = 21 \sqrt{3} - 5 \sqrt{ \frac{1}{3} } + 9 \sqrt{ \frac{1}{3} } \\ \\ =21 \sqrt{3} \times \frac{ \sqrt{3} }{ \sqrt{3} } - 5 \sqrt{ \frac{1}{3} } + 9 \sqrt{ \frac{1}{3} } \\ \\ =21 \times \frac{3}{ \sqrt{3} } - 5 \sqrt{ \frac{1}{3} } + 9 \sqrt{ \frac{1}{3} } \\ \\ =63 \sqrt{ \frac{1}{3} } - 5 \sqrt{ \frac{1}{3} } + 9 \sqrt{ \frac{1}{3} } \\ \\ = \sqrt{ \frac{1}{3} } \times \bigg(63 - 5 + 9 \bigg) \\ \\ = \sqrt{ \frac{1}{3} } \times 67 \\ \\ = 67 \sqrt{ \frac{1}{3} }$

Answer 2

$\huge \underline \mathfrak {Solution:-}$

$3 \sqrt{147} - 5 \sqrt{ \frac{1}{3} } + 9 \sqrt{ \frac{1}{3} } \\ \\ = 3 \sqrt{3 \times 3\times 7 \times 7 \times \frac{1}{3} } + \sqrt{ \frac{1}{3} } (9 - 5) \\ \\ = 3 \times 3 \times 7 \sqrt{ \frac{1}{3} } + 4 \sqrt{ \frac{1}{3} }\\ = 63\sqrt{ \frac{1}{3} } + 4 \sqrt{ \frac{1}{3} }\\ \\ = \sqrt{ \frac{1}{3} } (63 + 4)\\ \\ = \sqrt{ \frac{1}{3} } (67) \\ \\ = 67 \sqrt{ \frac{1}{3} }$