SOLVING RADICALS

Unit 4 Radicals

Steps to solve radical equations

A radical equation is a equation with a variable under the radical sign!

STEPS:1) Isolate radical2) get rid of radical3) solve4) check

“Square a square root”

“Cube a cube root”ETC…

Solve each radical equation

Find all solutions.

8323 x

Answer: X = 14

3515 3 x

Answer: X = 342

SOLVE

Remember rational exponents represents radicals

To remove rational exponents raise each side the reciprocal power

Exponent like this is the same as a radical. 251)1(3 5

3

x

Answer: X=31

POWERINDEX

251)1(35 3 x

Solve

Solve

xx 57

Answer: X = -3

When X’s on both sides of

equation solve by graphing!

To solve by graphing:1)Graph2) Find x-intercepts

Word problem

You can model time, t in seconds, an object takes to reach the ground falling from height H, in meters by the equation:

If an object takes 7 seconds to fall to the ground, what was the initial height?

If an object takes 10 seconds?

How long will it take an object to hit the ground from a initial height of 100ft?

81.9

2)(

HHt

Objects falling hammer vs. feather

practice

Pg 394 #9-21 odd 26, 29, 32

Solving radicals

62 xx

VIDEO SOLUTION:

The solution/root/zero to a function is where the graph crosses the x-axis

Graph and find the intersections = solutions

Word problem

For a meteor crater in Arizona, the formula relates the diameter d of the rim(in meters) to the volume V (in cubic meters). What is the volume of the crater if the diameter is 1200 meters

3

3.02V

d

3

3.021200V

Solve by graphing or

by hand?

By hand will be easier

3

3.0600

V

3.06003

V

Cube both sides

000,800,646003.0 3 V

Applying radicals to problems

Radius of a sphere can be measured using the formula:

Find the radius if the volume is 250 ft3

Find the volume if the radius is 6 (K.A. video)

Pg. 365 #35, 36

3

4

3

V

r

Word problem

You can model the population of a Texas town between the years 1970 & 2005 by the function below. x is the year. In what year did the town have a population of 250,000?

3 1950000,75)( xxp

3 1950000,75000,250 x

3 19503

10 x

1950037.37 x

037.1987x

Practice

Pg 395 #24,25,45*,60Pg 418 #24, 54