radicals review. parts coefficient radical sign radicand – the number underneath the radical sign...

Radicals Review

Parts

72 Coefficient

Radical Sign

Radicand – the number underneath the radical

sign

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

2432

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.

3

Examples 72

Examples 443

Examples 1126

Your Turn:

Write problems 1 – 6 in simplest radical form.

1. 2.

3. 4.

5. 6.

Your Turn:

What about…

√18 𝑥2

Or…

3√25 𝑥6

Or Even…

5 𝑥√32𝑥11

Your Turn:

3√ 48𝑚7 6 √144 𝑥3 𝑦5

Multiplying Radicals

Multiply like parts coefficients * coefficients radicand * radicand

Simplify the radical if necessary

Examples 25142

Examples7x4x25

Examples )532(5

7. 8.

9. 10.

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

2

2

1

MonomialAn 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