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

6\( \sqrt{45} \) + 4\( \sqrt{5} \)
6\( \sqrt{9 \times 5} \) + 4\( \sqrt{5} \)
6\( \sqrt{3^2 \times 5} \) + 4\( \sqrt{5} \)
(6)(3)\( \sqrt{5} \) + 4\( \sqrt{5} \)
18\( \sqrt{5} \) + 4\( \sqrt{5} \)

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

First, solve for \( \left|z + 3\right| \):

\( \left|z + 3\right| \) + 4 = 9
\( \left|z + 3\right| \) = 9 - 4
\( \left|z + 3\right| \) = 5

The value inside the absolute value brackets can be either positive or negative so (z + 3) must equal + 5 or -5 for \( \left|z + 3\right| \) to equal 5:

So, z = -8 or z = 2.

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 add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-9y² + 7y²
(-9 + 7)y²
-2y²

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

1,130,000 in scientific notation is 1.13 x 10⁶