Simplify each expression. (2)/(√(3)+√(8))

Name: Problem 59, Chapter 10: Algebra 1 Common Core
Uploaded: 2020-04-03T04:14:01-08:00
Duration: 2 min 59 s
Channel: Julie Silva
Description: Simplify each expression. (2)/(√(3)+√(8))

Key Concepts

Multiplying by the Conjugate

When the denominator is a binomial containing radicals, multiplying the numerator and denominator by the conjugate of the denominator is a standard technique. The conjugate is formed by changing the sign between the two terms, which allows the use of the difference of squares formula to eliminate the radical terms in the denominator.

Rationalizing the Denominator

This concept involves rewriting a fraction so that the denominator does not contain any radicals. It is an important step in algebra that makes expressions easier to work with and compare, and often serves as a prerequisite for further simplification or operations on the expression.

Simplification of Radical Expressions

This concept includes combining like radicals, reducing square roots to their simplest form, and recognizing perfect squares within the radicand. It is a fundamental skill in algebra that ensures expressions are presented in their simplest and most useful form.

Transcript

00:01 We're being asked to simplify the given expression.

00:03 Well, the issue we have in this problem is that we have radicals in the denominator of our fraction.

00:08 And remember, when we're simplifying, we cannot have any radicals left in the denominator.

00:13 Well, to get rid of them, what we're going to do is we're going to multiply the numerator and the denominator by the conjugate of the denominator.

00:21 Well, the conjugate is going to be the square of the three minus the square of the v.

00:25 So we're going to multiply the numerator and the denominator by the square of the denominator.

00:30 3 minus the square of the v.

00:33 And again, same thing in the denominator.

00:35 We're going to multiply by the square of the 3 minus the square of the ve.

00:39 And so i sometimes like to put this term in the parentheses just so i can see what i'm multiplying.

00:44 So in the numerator, we need to distribute the two to both of these terms.

00:49 Well, 2 times root 3 is equal to 2 root 3, and 2 times negative root 8 is negative 2 root 8.

01:00 Now in our denominator we need to use the foil method.

01:04 So first we need to multiply root 3 times root 3, well root 3 times root 3 is root 9.

01:11 Next we need to multiply root 3 times negative root 8, which is negative root 24.

01:18 Then we multiply positive root 8 times positive 3, which is positive root 24.

01:25 And lastly, root 8 times negative root 8 is negative root 64.

01:31 And now we just need to simplify as much as possible...

Please give Ace some feedback