If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Algebra (all content)>Unit 10

Lesson 8: Multiplying binomials by polynomials

# Multiplying binomials with radicals (old)

An old video Where Sal multiplies and simplifies (x²-√6)(x²+√2). Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• Is there such a thing as a principle cube root?
• , actually, there is.
Although every real number has one and only one real cube root, it has two more roots than are imaginary or complex.
Just a warning: This gets pretty technical. Learn about imaginary numbers first.

Say we have x^3 = 1, solve for x. (This means x is the cube root of 1)

The possible values for x:
x = 1
x = -1/2 + sqrt(3)/2 i
x = -1/2 - sqrt(3)/2 i

This is how the 2nd answer works out, and you

can do the same process to the 3rd answer.

x = -1/2 + sqrt(3)/2 i
x^3 = (-… (readmoreof this comment)
(1 vote)
• What's the difference between the principle square root and the normal square root?
• Great question! When someone simply says or refers to a "square root" of a number, they are not specifying whether or not they want to know the positive or negative root of that number. For example:
The square root of 25 = 5 or -5 (because both 5*5 and -5*-5 are equal to 25)

The "principal square root" refers to ONLY the positive or absolute root value of the number. So:
The principle root of 25 = 5

Hope this helps!!
• With distributive property, how do you multiply a monomial by a binomail?
• You simply distribute the monomial through the binomial

Distributive property: a(b+c) = ab+ac
Ex: 3(x+y) = 3x+3y
• How do we know that the negative square root answer is wrong? Why do we only want the principle square root?
• The square root sign (√) means "principal square root". So if that sign is involved in the equation, you only want the principal square root because that's what the equation is asking for. If the equation is quadratic, such as x^2 = 16, then both square roots (here -4 and +4) are valid answers to the numerical equation, although one of them may be nonsensical if you consider what the equation is about. If you are finding a distance, for example, then a negative square root may not provide a sensible answer.
• This question may be in the wrong topic but I cannot find anything on here that talks about ADDING binomials together that include radicals.
an example: √(3-x) + √(x^2-1)
are equations like this able to be added together?
• the rules for adding radical expressions say that you can only add them if what's under the radicals is the same.
3√2 + 2√2 = 5√2 , for example.
• I don't understand FOIL...is it like PEMDAS?
• FOIL is just an acronym that people use when they first start multiplying things like (6+7) (3+5). It stands for First Outer Inner Last. But you do not have to follow that method like PEMDAS. Later on, you will learn the Distributive Property for solving equations like the one above. As you get to more advanced math, you will find yourself using FOIL not as often, but some people like it and it's a good place for teachers to start.
• How do you add two radicals together?
• You can only do it if they are the square root of the same number. So √2 + √5 cannot be simplified, but √3 + √3 can be simplified to 2√3.
• Why is square root 2 x square root 6 = square root 12?
• Ying,
It is easier to explain with square roots that are rational numbers.
The √9 * √4 = √(9*4) = √36 because
√(3*3) * √(2*2) = √(3*3*2*2) = 3*2 = 6

So
√(x) * √(y) = √(xy)

I hope that helps more than it confuses everyone.
• What does FOIL mean?
• F.O.I.L. is a mnenomic that stands for, "First, Outside, Inside, Last." It is a "trick" to help you remember how to multiply two binomials and is really just the distributive method. For an example lets look at (x+4)(x+5).
First + Outside + Inside + Last
First: x * x = x^2
Outside: x * 5 = 5x
Inside: 4 * x = 4x
Last: 4 * 5 = 20
x^2 + 5x + 4x + 20 = x^2 + 9x + 20