Question

√294-√150+2√6-3/√6 simplify this

Answer 1

Heya there !!
Here is the answer you were looking for:
$\frac{ \sqrt{294} - \sqrt{150} + 2 \sqrt{6} - 3}{ \sqrt{6} }$

On splitting we get,

$= \frac{ \sqrt{2 \times 3 \times 7 \times 7} - \sqrt{2 \times 3 \times 5 \times 5} + 2 \sqrt{6} - 3 }{ \sqrt{6} } \\ \\ = \frac{ \sqrt{ {7}^{2} \times 6 } - \sqrt{ {5}^{2} \times 6} + 2 \sqrt{6} - 3}{ \sqrt{6} } \\ \\ = \frac{7 \sqrt{6} - 5 \sqrt{6} + 2 \sqrt{6} - 3}{ \sqrt{6} }$

On rationalizing the denominator we get,

$= \frac{7 \sqrt{6} - 5 \sqrt{6} + 2 \sqrt{6} - 3}{ \sqrt{6} } \times \frac{ \sqrt{6} }{ \sqrt{6} } \\ \\ = \frac{ \sqrt{6} (7 \sqrt{6} - 5 \sqrt{6} + 2 \sqrt{6} - 3)}{ {( \sqrt{6} )}^{2} } \\ \\ = \frac{42 - 30 + 12 - 3 \sqrt{6} }{6} \\ \\ = \frac{14 - 10 + 4 - \sqrt{6} }{2} \\ \\ = \frac{8 - \sqrt{6} }{2}$

We know that √6 = 2.44

So,
Putting the value of √6 we get

$= \frac{8 - 2.44}{2} \\ \\ = 4 - 0.44 \\ \\ = 4.44$


Hope you understood !!

If you have any doubt regarding to my answer, feel free to ask me in the comment section ^_^

@Mahak24

Thanks...
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