How to Add and Subtract Square Roots and Cube Roots

TL;DR

To add and subtract square roots and cube roots, you can only combine like terms with the same radicands by adding or subtracting their coefficients. Additionally, you can simplify radicals to make them like terms before performing the operations, ensuring proper combinations based on their root types.

Transcript

in this lesson we're going to talk about adding and subtracting rational expressions what is 4 root 5 plus 6 root 5 what is that equal to now because the radicals are the same you can add the coefficient in front of it that is you can add four plus six which is ten so this is equal to ten root five let's say if you have four radical three plus six ... Read More

Key Insights

• 😑 Rational expressions with the same radicals can be added or subtracted by combining their coefficients.
• 🫚 Square roots and cube roots can be simplified to make them like terms for addition or subtraction.
• 😑 Distributing and foiling can be used to expand and simplify expressions with radicals.
• 🖕 The middle terms cancel out when expanding the product of conjugates.

Questions & Answers

Q: Can you add or subtract rational expressions with different radicals?

No, rational expressions can only be added or subtracted if they have the same radicals.

Q: How can you simplify rational expressions with the same radicals?

To simplify rational expressions with the same radicals, add or subtract the coefficients in front of the radicals.

Q: What do you do when you have rational expressions with different radicals?

You can simplify the radicals to make them the same before adding or subtracting the rational expressions.

Q: How can cube roots be simplified?

Cube roots can be simplified by finding the perfect cube factors of the numbers under the radicals and simplifying them.

Summary & Key Takeaways

• Rational expressions with the same radicals can be combined by adding or subtracting the coefficients in front of the radicals.

• Like terms containing the same radicals can be simplified by adding or subtracting the coefficients in front of the radicals.

• Radicals can sometimes be simplified to make them like terms for addition or subtraction.