Like radicals, adding and subtracting radical expressions, multiplying binomials with radicals, conjugates, and rationalizing the denominator.
In this lesson, variables under a radical stand for positive numbers.
Like radicals
You can't add \(\sqrt{2} + \sqrt{3}\) into a single radical, just as you can't add \(x + y\) into a single term. But you can combine \(4\sqrt{3} + 2\sqrt{3}\), just as \(4x + 2x = 6x\).
Radicals that don't look alike often become alike once you simplify them.
Multiplying binomials with radicals
Use the distributive property (FOIL) exactly as with polynomials.
Rationalizing the denominator
By convention, a simplified answer has no radical in the denominator. Removing it is called rationalizing the denominator: multiply the top and bottom by a carefully chosen factor (which is the same as multiplying by \(1\)).
Practice
Quick check
What is \(\sqrt{12} + \sqrt{3}\)?
\(\sqrt{12} = 2\sqrt{3}\), so the sum is \(2\sqrt{3} + \sqrt{3} = 3\sqrt{3}\).
Quick check
What is the conjugate of \(4 - \sqrt{7}\)?
Change only the sign between the two terms.
Finished this lesson?
Mark it as completed and it's saved on this device. Sign up to see it everywhere.