Applications of Radicals Part 1

Applications of Radicals Part 1

PREREQUISITE SKILLS

A. Operations on Radicals

Multiple Choice

Fill in the Blank

 $\left(\sqrt{5}+3\right)\left(\sqrt{5}-3\right)$  

Multiple Choice

Simplify.

 $\frac{4\sqrt{8x^5}}{2\sqrt{2x^2}}$  

•  $2x\sqrt{4x}$  

•  $2\sqrt{4x^3}$  

•  $4x\sqrt{x}$  

•  $4\sqrt{x^3}$  

Solving Linear Equations in One Variable

Fill in the Blank

Solve the value of x.

 $3x+2=23$  

Multiple Choice

 $x^2+4x+4=0$  

•  $x=2$  

•  $x=-2$  

•  $x=-2.\ 2$  

•  $x=4$  

Fill in the Blank

Find the value of x.

 $3-2x=4x-9$  

Math tip!

In solving radical equations, remember to always CHECK your answer. You may have solve it correctly, but you will only determine whether your answer is a solution when checked.

A ten-foot ladder is leaning against a wall. How far is the bottom of the ladder from the wall when the ladder reaches a height of 8 feet?

(Example 2) Try to answer this!

Math concepts that can be applied in solving the previous problem:

• Pythagorean Theorem

• Square Root Property

• Addition Property of Equality

• Solving Radical Equations

Let's Practice!

Solving radical equations.

Fill in the Blank

Find the value of x.

 $\sqrt{x}=2$  

Multiple Choice

Solve and simplify.

 $x\sqrt{3}=9$  

•  $\sqrt{27}$  

•  $3\sqrt{3}$  

•  $12$  

•  $9\sqrt{3}$  

Fill in the Blank

Solve the equation.

 $\sqrt{x}+1=5$  

Activity 1: Solve Me Right

Write your solution in a sheet of paper/online, attach to the assignment tab after.

Multiple Choice

The sides of a square are each 11 feet long. Find the length of the diagonal.

• $10\sqrt{2}\ ft$

• $11\sqrt{2}\ ft$

• $22\ ft$

• $\sqrt{11}\ ft$

Multiple Choice

A wall is 7 meters high. A boy stands 3 meters away from the base of the wall. How far is the top of the wall from the feet of the boy?

• $21\ m$

• $\sqrt{21}m\$

• $7\sqrt{3}\ m$

• $\sqrt{58}\ m$

Multiple Choice

The legs of a right triangle are congruent, and the hypotenuse is

 $7\sqrt{3}$  feet long. Find the length of each leg.

•  $49\sqrt{3}\ ft$  

•  $\frac{7\sqrt{6}}{2}ft$  

•  $147\ cm$  

•  $\frac{49\sqrt{3}}{2}ft$  

Multiple Choice

The algebraic expression  $\sqrt{\frac{h}{4}}$   represents the time, in seconds, that it takes an object to hit the ground if it is thrown at a height h, in meters. Determine how long it will take a mango dropped from a tree 8 meters tall to hit the ground.

•  $\sqrt{2}\ m$  

•  $\sqrt{8}\ m$  

•  $2\sqrt{2}m$  

• can't be determined
  

Don't forget to attach your solution in the assignment!

Study in Advance: Learning Module 29 pp. 6-8.