Radicals Review

Parts

72 Coefficient

Radical Sign

Radicand – the number underneath the radical

sign

RadicalPronounced: 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

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Getting Radicals into Simplest Radical Form

Steps1. Look for the largest perfect square that’s a factor of the radicand.

Getting Radicals into Simplest Radical Form

Steps2. Factor using the perfect square as one of the factors.

Getting Radicals into Simplest Radical Form

Steps3. Take the square root of the factor that’s a perfect square.

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Getting Radicals into Simplest Radical Form

Steps4. 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

Steps5. If there’s a number in front of the radical, multiply the square root by it.

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Examples 72

Examples 443

Examples 1126

Your Turn: Write problems 1 – 8 in simplest

radical form.

Multiplying Radicals Multiply like parts

coefficients * coefficients radicand * radicand

Simplify the radical if necessary

Examples 615

Examples 25142

Examples 23325

9. 10.

11. 12.

Your Turn:

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) 2

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MonomialAn expression with exactly one term

Examples: 3x –7x3

Non-Examples: 7x – 4 4y2 – 16y + 60