Question

solve................ ​

Answer 1

$\:\:\:\: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \huge\mathcal{\bf{\underline{\underline{\huge\mathcal{Answer}}}}}$

$\large\mathcal\red{\underline{solution}}$

$\large\mathcal\red{\underline{problem...1}}$

$\frac{4}{7 + 4 \sqrt{ 3} } \: \: \: (rationalizing \: the \: denominator)\\ = \frac{4(7 - 4 \sqrt{3} )}{(7 + 4 \sqrt{3} )(7 - 4 \sqrt{ 3} ) } \\ = \frac{28 - 16 \sqrt{3} }{7 {}^{2} - (4 \sqrt{3}) {}^{2} } \\ = \frac{28 - 16 \sqrt{3} }{49 - 48} \\ = 28 - 16 \sqrt{3}$

$\large\mathcal\red{\underline{problem...2}}$

$3 \sqrt{12} \times \sqrt{18} \\ = 3 \sqrt{4 \times 3} \times \sqrt{9 \times 2} \\ = 3 \times 2 \times 3 \sqrt{3 \times 2} \\ = 18 \sqrt{6}$

$\large\mathcal\red{\underline{problem...3}}$

$\sqrt{7 } - \frac{3}{5} \sqrt{7} + 2 \sqrt{7} \\ = 3 \sqrt{7} - \frac{3}{5} \sqrt{7} \\ = \frac{15 \sqrt{7} - 3 \sqrt{7} }{5} \\ = \frac{12 \sqrt{7} }{5}$

$\large\mathcal\red{\underline{problem...4}}$

$15.8989898989........ \\ = 15 + 0.89898989..... \\ = 15 + \frac{89}{99} \\ = \frac{99 \times 15 + 89}{99} \\ = \frac{1574}{99} \\ \: where \: \: now \: let \: x = 0.898989..... \\ 100x = 89.8989... \\ 100x = 89 + 0.8989.... \\ 100x = 89 + x \\ 100x - x = 89 \\ x = \frac{89}{99}$

$\large\mathcal\red{hope\: this \: helps \:you......}$