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4857750-508000No Calculators0No CalculatorsPerfect Squares and Square RootsA _______________________________ is the result of multiplying a whole number by itself. For example 64 is a perfect square because it is ______________The ______________________________ of a number is what you multiply by itself to get the number. For example, 8 is the square root of 64 because _____________________*Squaring and Square rooting are reverse operations!Example 1 What picture would you draw to show why 16 is 4?Example 2 What does 53 mean? What picture could you draw?Example 3 What is the value of each power?3443103-250.22Example 4 Why does it make sense that 250 000 is 100 times as much as 25?We can use facts like 10×10=and 100×100=to help estimate the square roots of larger numbers.For example, since 15 is close to then 1500 is close to and 150 000 is close to Example 5 Estimate each square root without a calculator. 8811036004900303000Example 6 Explain how you know that 250 cannot be a perfect square.Example 7 Which of these powers of 10 are perfect squares? Explain.100100010 000100 000Example 8 What is the least number you could multiply 2×2×4×5 by to make a perfect square? Explain.Example 9 How could factoring 57 600 as 64×36×25 help you figure out its square root?Properties of Powers*Powers of whole numbers grow very quickly. For example,34=8135=24336=729This is why there is the saying that something “grows exponentially” means that it increases faster and faster and faster*Powers of fractions or decimals less than 1 shrink as the exponent increases. For example,122=123=124=*Powers of negative numbers-22=-23=-24=-25=What conclusion can you make?Example 11 -2 is a positive number. What could be?Example 12 Order from least to greatest:133134132135Order from least to greatest:23242225What do you notice if you compare the answers to a) and b) ?Questions:Choose values to make these statements true: 4=92b) 68=36c) 253=6How would you write each of these as a single power? (There may be more than one way!)3×3×5×56×6×3×3×6×32×2×2×2×4×4×4×4 ................
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