All SAT Math Resources
Example Questions
Example Question #1 : How To Add Square Roots
If what is ?
Square both sides:
x = (32)2 = 92 = 81
Example Question #22 : Basic Squaring / Square Roots
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 , you can add them together to yield the final answer:
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 #2 : 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 or :
The other root values cannot be simply broken down. Now, combine the factors with :
This is your simplest form.
Example Question #23 : Basic Squaring / Square Roots
Solve for .
Note, :
Begin by getting your terms onto the left side of the equation and your numeric values onto the right side of the equation:
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 :