Multiply and simplify a radical expression 2 | Algebra I | Khan Academy

TL;DR

Dividing radical expressions can be simplified by dividing the whole expressions first, then simplifying the coefficients and variables separately.

Transcript

We're asked to divide and simplify. And we have one radical expression over another radical expression. The key to simplify this is to realize if I have the principal root of x over the principal root of y, this is the same thing as the principal root of x over y. And it really just comes out of the exponent properties. If I have two things that I ... Read More

Key Insights

• 😑 Dividing a radical expression can be simplified by dividing the whole expressions first and then simplifying coefficients and variables separately.
• 🧑‍🏭 Simplifying coefficients involves finding the greatest common factor and dividing both numerator and denominator by it.
• 🧑‍🏭 Simplifying variables requires canceling out common factors and combining like terms.

Questions & Answers

Q: How do you simplify a radical expression divided by another radical expression?

To simplify, divide the whole expressions first, then simplify the coefficients and variables separately.

Q: How do you simplify the coefficients in a radical expression?

Find the greatest common factor of the coefficients and divide both the numerator and denominator by it.

Q: How do you simplify the variables in a radical expression?

Cancel out common factors between the numerator and denominator variables, and combine any like terms.

Q: Can you further simplify a radical expression by taking out perfect square factors?

Yes, if desired, you can take out any perfect square factors from the radical sign to simplify the expression further.

Summary & Key Takeaways

• To simplify a radical expression divided by another radical expression, divide the whole expressions first and then simplify the coefficients and variables separately.

• Simplify the coefficients by finding the greatest common factor and dividing both numerator and denominator by it.

• Simplify the variables by cancelling out common factors and combining like terms.

• If desired, further simplify the expression by taking out any perfect square factors from the radical sign.