square roots irrational numbers - math 10 · •irrational number cannot be written as a fraction...
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Square Roots and
Irrational Numbers
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The square of an integer is a perfect square.
The opposite of squaring a number is taking the square root.
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Example
• For example asks what number multiplied by itself is equal to 81? That number is 9.
Is there another solution to that problem?
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Example
• For example asks what number multiplied by itself is equal to 81? That number is 9.
Is there another solution to that problem?Yes, 9 is also a solution.
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Simplify each square root
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Simplify each square root
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Simplify each square root
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Squares and roots• Here is a list that will be helpful:
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• Do you see that squares and square roots are inverses (opposites) of each other?
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Estimating square roots
• Once we have memorized these squares and their roots, we can estimate square roots that are not perfect squares
• For example, what about ?
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Estimating square roots
• We find the two perfect squares that are before and after the square root of 8. . .
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• Look at them on a number line:
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Estimating square roots
• We can see that is between 2 and 3 but is closer to 3. We would say that is approximately 3.
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TRY THIS:Estimate to the nearest whole number
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TRY THIS:Estimate to the nearest whole number
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TRY THIS:Estimate to the nearest whole number
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TRY THIS:Estimate to the nearest whole number
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Natural Numbers: N = { 1, 2, 3, …}
Whole Numbers: W = { 0, 1, 2 , 3, ...}
Integers: I = {….. 3, 2, 1, 0, 1, 2, 3, ...}
Number Systems
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Number Systems Cont…
Real Numbers: R = {all rational and irrational}
Imaginary Numbers: i = {sq. roots of negative
Complex Numbers: C = {real and imaginary numbers}
Rational Numbers:
Irrational Numbers: Q = {nonterminating, nonrepeating decimals}
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Examples• Natural #s: {1,…67,…280,…}• Whole #s: {0,1,2,…}• Integers: {…899,2,0,1989,…} • Rational #s: ½, 1/9, 0.33 (terminating or repeating decimals)• Irrational #s: √7, π = 3.14159265 3589 7932384626433832795… (nonterminating, nonrepeating)
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• Rational number can be written as a fraction
• Irrational number cannot be written as a fraction because:• it is a nonterminating decimal• it is a decimal that does NOT repeat
* The square roots of ALL perfect squares are rational.
* The square roots of numbers that are NOT perfect squares are irrational.
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• Rational #s: ½, 1/9, 0.33 (terminating or repeating decimals)•• Irrational #s: √7, π = 3.14159265 3589 7932384626433832795… (nonterminating, nonrepeating)
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Try This: Identify each number as rational or irrational
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Try This: Identify each number as rational or irrational
Irrational
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Try This: Identify each number as rational or irrational
Irrational
Rational
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Try This: Identify each number as rational or irrational
Irrational
Rational
Rational
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Try This: Identify each number as rational or irrational
Irrational
Rational
Rational
Rational
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Try This: Identify each number as rational or irrational
Irrational
Rational
Rational
Rational
Irrational
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COPY AND COMPLETE
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