Question

Those are the math questions I need the answers of ​

Answer 1

Answer:

1)

$12\sqrt{18}-3\sqrt{50}+\sqrt{32}$

$12\sqrt{9}\sqrt{2}-3\sqrt{25} \sqrt{2} +\sqrt{16} \sqrt{2}$

$12\times3\sqrt{2} -3\times5\sqrt{2}+4\sqrt{2}$

$36\sqrt{2}-15\sqrt{2}+4\sqrt{2}$

$25\sqrt{2}$

2)

$\frac{1}{5+2\sqrt{6}}$

Multiply $5-2\sqrt{6}$:

$\frac{1\times \left(5-2\sqrt{6}\right)}{\left(5+2\sqrt{6}\right)\left(5-2\sqrt{6}\right)}$

Apply Difference of Squares formula: $(a+b)(a-b)=a^2-b^2$

$\frac{5-2\sqrt{6}}{5^2-\left(2\sqrt{6}\right)^2}$

$\frac{5-2\sqrt{6}}{25-2^2\left(\sqrt{6}\right)^2}$

$\frac{5-2\sqrt{6}}{25-4\times6}$

$\frac{5-2\sqrt{6}}{1}$

${5-2\sqrt{6}}$

a = 5, b = -2