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Introduction to Roots Test
About Introduction to Roots:

We previously learned that squaring a number tells us to multiply the number by itself. When we ask for the square root of a number, we are performing the opposite operation. The square root of a number such as 9 is a number that when multiplied by itself gives us 9 back. The answer would be 3 or (-3).

Test Objectives:

•Demonstrate the ability to find the square root of a number

•Demonstrate the ability to find a cube root or higher level root of a number

•Demonstrate the ability to determine whether a number is rational, irrational, or not real

Introduction to Roots Test:




#1:


Instructions: Simplify.


a) $$\sqrt9$$


b) $$-\sqrt{9}$$


c) $$\sqrt{-9}$$


d) $$\sqrt{64}$$


e) $$-\sqrt{64}$$


f) $$\sqrt{-64}$$


g) $$\sqrt[3]{125,000}$$


h) $$-\sqrt[3]{125,000}$$


i) $$\sqrt[3]{-125,000}$$


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#2:


Instructions: Simplify.


a) $$\sqrt[4]{-1}$$


b) $$\sqrt[3]{-8}$$


c) $$\sqrt{784}$$


d) $$\sqrt[5]{1024}$$


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#3:


Instructions: Square each radical expression.


a) $$\sqrt{11}$$


b) $$\sqrt{5x}$$


c) $$\sqrt{3x^2-2x-1}$$


d) $$\sqrt{\frac{5x^4-3x-7}{3x}}$$


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#4:


Instructions: Determine if each is rational, irrational, or not real.


a) $$\sqrt{169}$$


b) $$\sqrt{200}$$


c) $$\sqrt[3]{49}$$


d) $$\sqrt[4]{-16}$$


e) $$\sqrt{\frac{1}{4}}$$


f) $$\sqrt[8]{-13}$$


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#5:


Instructions: Simplify.


a) $$\sqrt{3^2+4^2}$$


b) $$\sqrt{8^2-28}$$


c) $$\sqrt{12^2+5^2}$$


d) $$\sqrt[3]{(-1)^3+6^3-207}$$


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Written Solutions:




#1:


Solution:


a) 3


b) -3


c) not real


d) 8


e) -8


f) not real


g) 50


h) -50


i) -50


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#2:


Solution:


a) not real


b) -2


c) 28


d) 4


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#3:


Solution:


a) 11


b) 5x


c) 3x2 - 2x - 1


d)


5x4 - 3x - 7
3x

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#4:


Solution:


a) rational


b) irrational


c) irrational


d) not real


e) rational


f) not real


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#5:


Solution:


a) 5


b) 6


c) 13


d) 2


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