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

6\( \sqrt{175} \) + 3\( \sqrt{7} \)
6\( \sqrt{25 \times 7} \) + 3\( \sqrt{7} \)
6\( \sqrt{5^2 \times 7} \) + 3\( \sqrt{7} \)
(6)(5)\( \sqrt{7} \) + 3\( \sqrt{7} \)
30\( \sqrt{7} \) + 3\( \sqrt{7} \)

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

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

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:

\( \sqrt{\frac{25}{16}} \)
\( \frac{\sqrt{25}}{\sqrt{16}} \)
\( \frac{\sqrt{5^2}}{\sqrt{4^2}} \)
\( \frac{5}{4} \)
1\(\frac{1}{4}\)

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

To raise a term with an exponent to another exponent, retain the base and multiply the exponents: