Math - Simplifying Radicals | Summary and Q&A

TL;DR

Learn how to simplify radical expressions without a calculator using the properties of perfect square trinomials.

Key Insights

• ❎ Simplifying radical expressions without a calculator involves checking if they match the form a squared plus b squared minus 2ab.
• ❎ Values for a and b can be found by setting b as the square root of the constant term and solving for a using the coefficient of the square root term.
• ❎ When a squared plus b squared equals the constant term, the expression can be simplified to a minus b or a plus b.

Transcript

consider this problem what is the square root of 21 minus 8 square root 5 how would you simplify this radical without the use of a calculator feel free to pause the video and think about it the square root of let's say 8 squared is 8. in order to simplify this it needs to be in the right form so the square root of a plus b squared is going to be a ... Read More

Questions & Answers

Q: How do you simplify a radical expression without a calculator?

To simplify a radical expression without a calculator, you need to check if it matches the form a squared plus b squared minus 2ab. If it does, you can find values for a and b and simplify the expression accordingly.

Q: How do you check if a radical expression is in the right form?

To check if a radical expression is in the right form, you compare it to the form a squared plus b squared minus 2ab. If they match, you can simplify the expression using the properties of perfect square trinomials.

Q: How do you find values for a and b to simplify a radical expression?

To find values for a and b, you set b as the square root of the constant term and solve for a using the coefficient of the square root term. If a squared plus b squared equals the constant term, the expression can be simplified to a minus b or a plus b.

Q: How do you verify if a simplified radical expression is correct?

To verify if a simplified radical expression is correct, you can multiply it by itself and check if it equals the original expression. If they match, the simplification is correct.

Summary & Key Takeaways

• In order to simplify a radical expression without a calculator, it needs to be in the right form, where the square root of a plus b squared simplifies to a plus b and the square root of a minus b squared simplifies to a minus b.

• To check if a radical expression is in the right form, you can compare it to the form a squared plus b squared minus 2ab. If they match, you can simplify the expression.

• The key is to find values for a and b, by setting b as the square root of the constant term and solving for a using the coefficient of the square root term. If the resulting a squared plus b squared equals the constant term, the expression can be simplified to a minus b or a plus b.