SOLUTION: radical 50 + radical 18

Algebra ->  Radicals -> SOLUTION: radical 50 + radical 18      Log On


   

Question 116380: radical 50 + radical 18
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
You are given:
.
sqrt%2850%29+%2B+sqrt%2818%29
.
To simplify this you can use the rule that says:
.
sqrt%28A%2AB%29+=+sqrt%28A%29%2Asqrt%28B%29
.
Applying that rule to sqrt%2850%29 we can break the 50 up into the product of 25*2.
So we can say that sqrt%2850%29+=+sqrt%2825%2A2%29+=+sqrt%2825%29%2Asqrt%282%29
.
But sqrt%2825%29+=+5. So we can substitute 5 for sqrt%2825%29 and the problem simplifies
further:
.
sqrt%2850%29+=+sqrt%2825%2A2%29+=+sqrt%2825%29%2Asqrt%282%29+=+5%2Asqrt%282%29
.
Now let's do the same thing for sqrt%2818%29. Factor 18 so that you have:
.
sqrt%2818%29+=+sqrt%289%2A2%29+=+sqrt%289%29%2A+sqrt%282%29
.
And sqrt%289%29+=+3 so this part of the problem simplifies further to:
.
sqrt%2818%29+=+sqrt%289%2A2%29+=+sqrt%289%29%2A+sqrt%282%29+=+3%2Asqrt%282%29
.
Put the two parts of the problem together ...
.
sqrt%2850%29+%2B+sqrt%2818%29+=+5%2Asqrt%282%29+%2B+3%2Asqrt%282%29
.
If you factor sqrt%282%29 from the two terms on the right side you get:
.
5%2Asqrt%282%29+%2B+3%2Asqrt%282%29+=+%285+%2B+3%29%2Asqrt%282%29+=+8%2Asqrt%282%29
.
So the answer to this problem is:
.
sqrt%2850%29+%2B+sqrt%2818%29+=+8%2Asqrt%282%29
.
Hope this helps you to understand one of the rules that can be used in simplifying
radicals.
.