To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-1y² + 2y²
(-1 + 2)y²
y²

To subtract these radicals together their radicands must be the same:

6\( \sqrt{112} \) - 8\( \sqrt{7} \)
6\( \sqrt{16 \times 7} \) - 8\( \sqrt{7} \)
6\( \sqrt{4^2 \times 7} \) - 8\( \sqrt{7} \)
(6)(4)\( \sqrt{7} \) - 8\( \sqrt{7} \)
24\( \sqrt{7} \) - 8\( \sqrt{7} \)

Now that the radicands are identical, you can subtract them:

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{9}{64}} \)
\( \frac{\sqrt{9}}{\sqrt{64}} \)
\( \frac{\sqrt{3^2}}{\sqrt{8^2}} \)
\(\frac{3}{8}\)

To multiply terms with radicals, multiply the coefficients and radicands separately:

9\( \sqrt{9} \) x 2\( \sqrt{2} \)
(9 x 2)\( \sqrt{9 \times 2} \)
18\( \sqrt{18} \)

Now we need to simplify the radical:

18\( \sqrt{18} \)
18\( \sqrt{2 \times 9} \)
18\( \sqrt{2 \times 3^2} \)
(18)(3)\( \sqrt{2} \)
54\( \sqrt{2} \)

A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:

48,000 fans x \( \frac{2}{3} \) = \( \frac{96000}{3} \) = 32,000 fans.