Square Roots and Rational and Irrational Numbers n
Square Roots and Rational and Irrational Numbers
n https: //www. brainpop. com/math/number sandoperations/squareroots/
1 2 3 The square of an integer is a perfect square. The opposite of squaring a number is taking the square root.
Example n For example asks what number multiplied by itself is equal to 81? That number is 9. Is there another solution to that problem?
Example n 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.
Simplify each square root
Simplify each square root 10
Simplify each square root 10 -4
Squares and roots n Here is a list that will be helpful:
n Do you see that squares and square roots are inverses (opposites) of each other?
Estimating square roots n Once we have memorized these squares and their roots, we can estimate square roots that are not perfect squares n For example, what about ?
Estimating square roots n n n We find the two perfect squares that are before and after the square root of 8. . . and Look at them on a number line: 2 3
Estimating square roots n We can see that is between 2 and 3 but is closer to 3. We would say that is approximately 3. 2 3
TRY THIS: Estimate to the nearest whole number
TRY THIS: Estimate to the nearest whole number 5
TRY THIS: Estimate to the nearest whole number 5 -9
TRY THIS: Estimate to the nearest whole number 5 -9 7
Rational vs. Irrational Numbers n https: //www. brainpop. com/math/number sandoperations/rationalandirrationalnu mbers/ n https: //www. youtube. com/watch? v=Qte m. Vfz. SGBA
n Rational number- can be written as a fraction of two integers n Irrational number- cannot be written as a fraction of two integers because: • it is a non-terminating 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.
Key Things to Remember: n The sum or product of a rational number is rational. n The sum of a rational number and irrational number is irrational. n The product of a nonzero rational number and an irrational number is irrational.
Try This: Identify each number as rational or irrational
Try This: Identify each number as rational or irrational Irrational
Try This: Identify each number as rational or irrational Irrational Rational
Try This: Identify each number as rational or irrational Irrational Rational
Try This: Identify each number as rational or irrational Irrational Rational
Try This: Identify each number as rational or irrational Irrational Rational Irrational
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