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11-1 & 11-2 Squares and Square Roots (pgs 470-477)

11-1 & 11-2 Squares and Square Roots (pgs 470-477). Indicator: N9  Solve problems using exponents and square roots. To Square a number: multiply the number by itself. Perfect Squares : Squares whose side lengths (square roots) are rational numbers. (ex: 1, 4, 9, 16, 25….)

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11-1 & 11-2 Squares and Square Roots (pgs 470-477)

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  1. 11-1 & 11-2 Squares and Square Roots(pgs 470-477) Indicator: N9  Solve problems using exponents and square roots

  2. To Square a number: multiply the number by itself. • Perfect Squares: Squares whose side lengths (square roots) are rational numbers. (ex: 1, 4, 9, 16, 25….) • Radical Sign: √ Symbol used to indicate the square root of a number.

  3. Remember: Squaring and square rooting are inverse operations so they are located on the same calculator key (You just need to push the 2ndkey to get to the square root) Press in the #, 2nd, then x². • 4•4 and (-4)•(-4) both equal 16, so 16 has two square roots √16 is asking for the positive or principal root = 4. -√16 is asking for the negative root = -4 +√16 is asking for both = 4 & -4

  4. Find the square of 5 5•5 =25 • What is 19 squared 192 = 361 • Find √36 √36 = 6 • Find √ 676 √ 676= 26

  5. Using squares and square roots The formula for kinetic energy = ½mv2 If a 6kg ball is soaring through the air at 5m/s, what is its kinetic energy? = ½ • mv2 = ½ • 6kg• (5m/s)2 = ½ • 6kg•25m2/s2 =75kg•m2/s2

  6. To Estimate… (without a calculator) • First- remember that the square root of a perfect square is a rational number. • To find an estimate for the square root of a number that is not a perfect square… • Let’s recall some of the perfect squares- 1, 4, 9, 16, 25, 36, 49, 64, 81, 100…

  7. Continue estimating • For example: Estimate √96 to the nearest whole number • Think of your perfect squares… 1, 4, 9, 16, 25, 36, 49, 64, 81, 100… • 96 falls between 81 and 100 • Which is it closer to? • So, the best estimate for √96 is 10.

  8. To estimate… (with a calculator) • Remember: Press in the #, 2nd, then x² • You can be a little more precise here… • For example: Use a calculator to find the value of √37 to the nearest tenth. • = 6.08276253… Rounds to ≈ 6.1

  9. Assignment 11-1/ 472 – 473/ 12-28e,29-51 11-2/ 477/ 17-24, 29-32, 35-44

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