About Square Root:
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
#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:
Solutions:
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:
Solutions:
a) not real
b) -2
c) 28
d) 4
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#3:
Solutions:
a) 11
b) 5x
c) 3x2 - 2x - 1
d)
5x4 - 3x - 7 |
3x |
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#4:
Solutions:
a) rational
b) irrational
c) irrational
d) not real
e) rational
f) not real
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#5:
Solutions:
a) 5
b) 6
c) 13
d) 2