SOLUTION: The section is adding/subtracting radicals. My problem is subtracting. The equation is: The sqaure root of 120 - The square root of 270

SOLUTION: The section is adding/subtracting radicals. My problem is subtracting. The equation is: The sqaure root of 120 - The square root of 270 - The square root of 300. Can you help me?

Question 78933This question is from textbook Algebra
: The section is adding/subtracting radicals. My problem is subtracting.
The equation is: The sqaure root of 120 - The square root of 270 - The square root of 300. Can you help me? This question is from textbook Algebra

Found 2 solutions by stanbon, tutor_paul:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
sqaure root of 120 - The square root of 270 - The square root of 300.
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Factor each radicand into the product of a perfect square and another number:
= sqrt(4*30) - sqrt(9*30) - sqrt(100*3)
= 2sqrt30 -3sqrt30 - 10sqrt3
= -sqrt30 -10sqrt3
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Cheers,
Stan H.
Answer by tutor_paul(519) (Show Source): You can put this solution on YOUR website!

Before you can add or subtract radicals, you need to have the same quantity under the square root symbol. Obviously, you don't have that right now with this problem, so let's try to simplify each radical to see if we can make that happen:
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Looking at the first term, you can rewrite it as:

Now I see that I can pull a 2 out from under this radical, since . So I can rewrite it as:

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Similarly for the next term, you can rewrite it as:

I can pull a 3 out of this radical, since
This leaves me with:

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Finally for the last term,

This can be written using the same logic as above as:

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So after all that, I can rewrite the original problem as:

Now, you can see that two of these terms can be combined, since they both have 30 under the radical. So, this can be simplified to be:

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Good Luck,
tutor_paul@yahoo.com
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