Question
Add. Write your answer in simplest form. negative 4 radical 14+9 radical 14
Answers
GPT-4 Turbo
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
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
cyan
subtract. Write your answer in simplest form.
negative radical 135 minus 10 radical 15
negative radical 135 minus 10 radical 15
GPT-4 Turbo
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
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