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

5\( \sqrt{12} \) + 7\( \sqrt{3} \)
5\( \sqrt{4 \times 3} \) + 7\( \sqrt{3} \)
5\( \sqrt{2^2 \times 3} \) + 7\( \sqrt{3} \)
(5)(2)\( \sqrt{3} \) + 7\( \sqrt{3} \)
10\( \sqrt{3} \) + 7\( \sqrt{3} \)

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

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.

48% of the water consumption is industrial use and 26% is personal use so (48% - 26%) = 22% more water is used for industrial purposes. 40,000 gallons are consumed daily so industry consumes \( \frac{22}{100} \) x 40,000 gallons = 8,800 gallons.

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

-x³ x 4x⁵
(-1 x 4)x^{(3 + 5)}
-4x⁸

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).