Add. Write your answer in simplest form. negative 4 radical 14+9 radical 14
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
subtract. Write your answer in simplest form.
negative radical 135 minus 10 radical 15
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
To simplify the expression, you can combine the terms that have the same radical. In this case, both terms have the radical √14.
So, we can rewrite the expression as:
(-4√14) + (9√14)
To combine these two terms, we add the coefficients. The coefficient of the first term is -4, and the coefficient of the second term is 9.
Now, let's add these coefficients:
(-4 + 9)√14 = 5√14
Therefore, the simplified form of the expression "-4√14 + 9√14" is "5√14".