Question

simplify the following by the denominator 7 root 3-5 root 2/ root 48​

Answer 1

Step-by-step explanation:

Here is the answer you were looking for:

\frac{7 \sqrt{3} - 5 \sqrt{2} }{ \sqrt{48} + \sqrt{18} } \\ \\ = \frac{7 \sqrt{3} - 5 \sqrt{2} }{ \sqrt{2 \times 2 \times 2 \times 2 \times 3} + \sqrt{2 \times 3 \times 3} } \\ \\ = \frac{7 \sqrt{3} - 5 \sqrt{2} }{2 \times 2 \sqrt{3} + 3 \sqrt{2} } \\ \\ = \frac{7 \sqrt{3} - 5 \sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} } \\ \\ on \: rationalizing \: the \: denominator \: we \: get \\ \\ = \frac{7 \sqrt{3} - 5 \sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} } \times \frac{4 \sqrt{3} - 3 \sqrt{2} }{4 \sqrt{3} - 3 \sqrt{2} } \\ \\ using \: the \: identity \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ = \frac{7 \sqrt{3} \times 4 \sqrt{3} - 7 \sqrt{3} \times 3 \sqrt{2} - 5 \sqrt{2} \times 4 \sqrt{3} + 5 \sqrt{2} \times 3 \sqrt{2} }{ {(4 \sqrt{3}) }^{2} - {(3 \sqrt{2}) }^{2} } \\ \\ = \frac{28 \times 3 - 21 \sqrt{6} - 20 \sqrt{6} + 15 \times 2 }{48 - 18} \\ \\ = \frac{84 - 41\sqrt{6} + 30}{30} \\ \\ = \frac{114 - 41 \sqrt{6} }{30}

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