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:

\( \sqrt{\frac{81}{25}} \)
\( \frac{\sqrt{81}}{\sqrt{25}} \)
\( \frac{\sqrt{9^2}}{\sqrt{5^2}} \)
\( \frac{9}{5} \)
1\(\frac{4}{5}\)

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

\( \frac{45\sqrt{6}}{9\sqrt{3}} \)
\( \frac{45}{9} \) \( \sqrt{\frac{6}{3}} \)
5 \( \sqrt{2} \)

If the tiger has consumed 100 pounds of food in 10 days that's \( \frac{100}{10} \) = 10 pounds of food per day. The tiger needs to consume 130 - 100 = 30 more pounds of food to reach 130 pounds total. At 10 pounds of food per day that's \( \frac{30}{10} \) = 3 more days.

The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.