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

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

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

4\( \sqrt{50} \) + 8\( \sqrt{2} \)
4\( \sqrt{25 \times 2} \) + 8\( \sqrt{2} \)
4\( \sqrt{5^2 \times 2} \) + 8\( \sqrt{2} \)
(4)(5)\( \sqrt{2} \) + 8\( \sqrt{2} \)
20\( \sqrt{2} \) + 8\( \sqrt{2} \)

Now that the radicands are identical, you can add them together:

The amount of flour you need is (3\(\frac{3}{8}\) - \(\frac{1}{2}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{27}{8} \) - \( \frac{4}{8} \)) cups
\( \frac{23}{8} \) cups
2\(\frac{7}{8}\) cups

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:

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