Simplifying square roots | Exponent expressions and equations | Algebra I | Khan Academy

TL;DR

Simplify 3 times the principal root of 500x to the third power by breaking down the expression into perfect squares and simplifying each part.

Transcript

Simplify 3 times the principal root of 500x to the third power. So what we're going to do here is try to break up this stuff that we have under the radical sign into some things that are perfect squares. And then we can separately take the square root of those things and leave the left overs inside of the radical sign. And the other thing we have t... Read More

Key Insights

• 💯 Breaking down complex expressions into perfect squares and non-perfect squares helps simplify calculations.
• 🫚 The principal root represents the positive square root of a number.
• 👻 Rewriting numbers and variables in terms of perfect squares allows for easier simplification.
• 🥡 The absolute value of x is used to ensure a positive result when taking the principal root.
• 👻 Multiplication can be done in any order, allowing for rearrangement of terms during simplification.
• 😑 Simplifying expressions involving radicals involves considering both the number and the variable part.
• 🫚 The principal root of a product can be simplified as the product of the principal roots of each factor.

Questions & Answers

Q: How can we simplify the principal root of 500x to the third power?

To simplify the expression, we break down the numbers and variables into perfect squares and non-perfect squares. We then take the principal root of each part separately.

Q: What is the principal square root?

The principal square root is the positive square root of a number. It is denoted by the radical sign (√).

Q: Why should we rewrite 500 as 100 times 5?

By rewriting 500 as 100 times 5, we can identify 100 as a perfect square (10 squared). This helps simplify the expression further.

Q: Why do we need to consider the absolute value of x when simplifying?

We take the absolute value of x to ensure that the result is always positive. The principal root only considers the positive square root.

Summary & Key Takeaways

• Break down 500x to the third power into perfect squares and non-perfect squares.

• Rewrite the expression as 3 times the principal root of (10 squared times 5) times the principal root of (x squared times x).

• Simplify each part by taking the principal root and rewriting the expression as 30 times the absolute value of x times the square root of 5x.