Question

Add. Write your answer in simplest form. negative 4 radical 14+9 radical 14

Answer 1

subtract. Write your answer in simplest form.
negative radical 135 minus 10 radical 15

Answer 2

When adding radical expressions, we do so by combining like terms. In this case, both terms are like terms because they include the same radical, radical 14 (√14).

Here is how you would combine them:

-4√14 + 9√14

Just like with regular numbers, you simply add the coefficients (the numbers in front of the radicals):

(-4 + 9)√14

Now, add the coefficients:

5√14

Thus, the expression in its simplest form is:

5√14

Answer 3

To subtract radical expressions, we first look to simplify the radicals to see if they can be expressed with like terms. Let's first simplify √135 to see if it has any factors that are perfect squares.

The number 135 can be factored into 9 and 15, where 9 is a perfect square. So we can write:

√135 = √(9*15)
= √9 * √15
= 3√15

Now we have:

-√135 - 10√15
=-3√15 - 10√15

With both terms now having the radical √15, they are like terms, and we can subtract the coefficients:

-3√15 - 10√15
= (-3 - 10)√15
= -13√15

Therefore, the expression in its simplest form is:

-13√15