SAT Math : How to add square roots
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Example Questions
Example Question #1 : How To Add Square Roots
If 
Square both sides:
x = (32)2 = 92 = 81
Example Question #11 : Square Roots And Operations
Simplify in radical form:
To simplify, break down each square root into its component factors:
You can remove pairs of factors and bring them outside the square root sign. At this point, since each term shares 
Example Question #1 : Square Roots And Operations
Simplify:
None of the other answers
Take each fraction separately first:
(2√3)/(√2) = [(2√3)/(√2)] * [(√2)/(√2)] = (2 * √3 * √2)/(√2 * √2) = (2 * √6)/2 = √6
Similarly:
(4√2)/(√3) = [(4√2)/(√3)] * [(√3)/(√3)] = (4√6)/3 = (4/3)√6
Now, add them together:
√6 + (4/3)√6 = (3/3)√6 + (4/3)√6 = (7/3)√6
Example Question #3 : Square Roots And Operations
Simplify the following expression:
Begin by factoring out each of the radicals:
For the first two radicals, you can factor out a 
The other root values cannot be simply broken down. Now, combine the factors with 
This is your simplest form.
Example Question #4 : Square Roots And Operations
Solve for 
Note, 
Begin by getting your 
Next, you can combine your radicals. You do this merely by subtracting their respective coefficients:
Now, square both sides:
Solve by dividing both sides by 
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