Introduction to Roots Test

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:

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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