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ALGEBRA UNIT 9-RADICALS

SIMPLIFYING RADICALS (DAY 1)

How can you determine if a number is perfect square?

Simplify the following:

1) 18 2) - 984 3) - 484

3

4) 122

1 5) 502 6) 27

PROCEDURE TO SIMPLIFY RADICALS (non-perfect squares):

1. List perfect squares from 1 to 200 out. (VIPS) (create a list)

2. Any # in front of the comes down to be multiplied into your final answer

3. Determine where the number under the (that you are simplifying) would

fall in this list.

4. Work UP the list to #1 to locate the largest perfect square that goes into

your number.

5. Once found, break up your original (house) by placing the largest

perfect square number found under the first sign and place its divisor

under the second sign.

6. Circle the perfect square. – IT IS SO PERFECT THAT IT _____________ OUT OF

THE HOUSE. (This number will get multiplied with any number that was

originally outside the sign. Carry remaining radical down to your

answer.

VIPS

LIST

2

7) 999 8) 323 9) 755

2

10) 25

4 11) 16.0 12) 5004

13) Given a right triangle with leg of 8 m and a hypotenuse of 12m, determine

the length of the other leg in simplest radical form.

14) Given a right triangle with a hypotenuse of 28 and a leg of 10. Find the length of

the missing leg in simplest radical form.

15. Given a right triangle with a leg of 8cm and a leg of 6cm. Find the length of the

hypotenuse in simplest radical form.

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SIMPLIFYING RADICALS CONT…(DAY 2)

1) 645 2) 482 3) 722

1

4) 128x2 5) 1765 6) 50d2

1 4

7) 1473 8) 5002 9) 24a5 2

VIPS

LIST

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10) The length of the hypotenuse of a right triangle is 13cm. One leg is 7cm, find the

length of the other leg in simplest radical form.

11) A woman casts a shadow of 11ft. The measure from the top of her head to the tip

of the shadow is 12.5ft. How tall is the woman to the nearest foot?

12) Given a right triangle with a hyptoneuse of 29 and a leg of 8, find the length of

the missing leg in simplest radical form.

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ADDING RADICALS/SUBTRACTING RADICALS (DAY 3)

SIMPLIFY:

1. 9+915 2. 63 - 68 3. 563234

4. Find the sum of 12x2 and 3x7 . 5. Subtract 86 from 323 .

6. What is the difference between 755

1and 482

7. The sides of a triangle are 45 , 180 , and 202 . Find the perimeter of the triangle

in simplest radical form.

8. The perimeter of a rectangle is 836 . The width of the rectangle is 23 . Find the

length of the rectangle in simplest radical form.

ADDING RADICALS/SUBTRACTING RADICALS:

(MUST HAVE SAME RADICALS TO COMPLETE OPERATIONS)

1. Simplify radical if necessary. (Must have same radical)

2. Add/Subtract COEFFICIENTS of LIKE RADICALS.

3. Attach/carry LIKE RADICAL to answer.

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MULTIPLIYING RADICALS (DAY 4)

Perform the indicated operation, put answer in simplest radical form, and state if the

answer is a rational or irrational number.

1. 15•63

2 2. 3•3 3. 3•63

4. 3•12 5. - 5•94

3 6. 37•85

Find the area of the figures below in simplest radical form.

7.

8. A patio has a length of 610 and a width of 204 . The contractor wants to buy

enough bags of concrete to fill this area. If each bag covers 9 square feet, how

many bags of concrete should he buy.

PROCEDURE FOR MULTIPLYING RADICALS:

1. MULTIPLY the COEFFICIENTS of each of the radicals.

2. MULTIPLY the RADICALS

3. SIMPLIFY final Answer

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DIVIDING RADICALS

Perform operation and Simplify:

1. 824 2. 4

36 3.

12

96

4. -4236

718 5. 24488 6. -

36

543

7. 24675

2815

8. The area A of a rectangle and the measure of its base b are given. Find the height

h of the rectangle expressed in simplest form. 52b606A

PROCEDURE FOR DIVIDING RADICALS:

1. DIVIDE the COEFFICIENTS

2. Determine radical position in final answer by comparing radicands. Radical

will stay in the position of where the larger radicand was originally located.

3. DIVIDE larger radicand number by smaller radicand number.

4. SIMPLIFY final Answer