Radicals Review

Pronounced: 2 times the square root of 7 OR 2 radical 7 Parts Radical Sign Radicand – the number underneath the radical sign Coefficient Radical Pronounced: 2 times the square root of 7 OR 2 radical 7

Simplest Radical Form When you cannot factor any more perfect squares from the radicand The radical cannot be simplified further We always want our answers to be in simplest radical form

Getting Radicals into Simplest Radical Form Steps 1. Look for the largest perfect square that’s a factor of the radicand.  

Getting Radicals into Simplest Radical Form Steps 2. Factor using the perfect square as one of the factors.

Getting Radicals into Simplest Radical Form Steps 3. Take the square root of the factor that’s a perfect square. 4

Getting Radicals into Simplest Radical Form Steps 4. Write the square root as the factor in front of the radical and leave the other factor under the radical.

Getting Radicals into Simplest Radical Form Steps 5. If there’s a number in front of the radical, multiply the square root by it. 3

Tips for Getting Radicals into Simplest Radical Form Always check if the radicand is perfect square! Check if factorable by common perfect squares – 4, 9, 16, or 25 If the radicand is prime (or if its only factors are prime), then it’s in simplest radical form Be persistent! You don’t have to find the largest perfect square the first time you factor the radicand

Examples

Examples

Examples

Your Turn: Write problems 1 – 6 in simplest radical form.

Your Turn: 1. 2. 3. 4. 5. 6.

What about… 18 𝑥 2

Or… 3 25 𝑥 6

Or Even… 5𝑥 32 𝑥 11

Your Turn: 3 48 𝑚 7 6 144 𝑥 3 𝑦 5

Multiplying Radicals Multiply like parts coefficients * coefficients radicand * radicand Simplify the radical if necessary

Examples

Examples

Examples

Your Turn: 7. 8. 9. 10.

Seek and Solve!!!

What is rationalizing? The process of algebraically removing a radical sign from one part of a fraction We generally rationalize the denominator (But we can rationalize the numerator.)

Why rationalize? The result is easier to estimate and understand Also shows up in solving limits (in calculus)

An expression with exactly one term Monomial An expression with exactly one term Examples: 3x –7x3 Non-Examples: 7x – 4 4y2 – 16y + 60

Rationalizing the Numerator Exact same process as rationalizing the denominator, except that we focus on the numerator instead of the denominator. Reappears in calculus