A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{6 x 3}{3 x 3} \) - \( \frac{8 x 1}{9 x 1} \)

\( \frac{18}{9} \) - \( \frac{8}{9} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{18 - 8}{9} \) = \( \frac{10}{9} \) = 1\(\frac{1}{9}\)

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:

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

If the tiger has consumed 48 pounds of food in 8 days that's \( \frac{48}{8} \) = 6 pounds of food per day. The tiger needs to consume 84 - 48 = 36 more pounds of food to reach 84 pounds total. At 6 pounds of food per day that's \( \frac{36}{6} \) = 6 more days.