Lesson 9.1 Square Roots Essential Question: How do you find and approximate square roots of numbers?

Before we start… You want to put a fence around a square plot of land that has an area of 2500 square meters. What is the length of one side of the land? How much fencing do you need?

𝑛 and − 𝑛 What is a square root? A number m is a square root of a number n if 𝑚2 =𝑛. Every positive number has a positive square root and a negative square root. 𝑛 and − 𝑛

radical symbol radicand

How do you evaluate a square root? You need to find a number b such that 𝑏 2 =𝑎

− 49 ± 1

144 256

Perfect Squares The square of an integer. If the radicand is a whole number that is not a perfect square, you need to approximate the square root.

How do you approximate a square root? Two ways: Approximate the nearest integer (what perfect square is the whole number closest to) Use a calculator to get a decimal approximation

10 − 18

How do you solve equations using square roots? Take the square root of both sides You get two answers: a positive and a negative

Solve 𝑥 2 =64

Solve 𝑡 2 =36

Solve 𝑘 2 =121

Solve 𝑦 2 −15=10

Solve 𝑥 2 +7=16

What is a radical expression? An expression that involves a radical sign

Evaluate 2 𝑎+ 𝑏 2 when 𝑎=11 and 𝑏=5

Evaluate 𝑎+𝑏 when 𝑎=12 and 𝑏=4

Evaluate 𝑏 2 −𝑎 when 𝑎=27 and 𝑏=6

Physics An amusement park ride includes a free fall drop of 272 feet Physics An amusement park ride includes a free fall drop of 272 feet. You can use the equation 𝑑=16 𝑡 2 to determine the time t in seconds that it takes a dropped object to fall a distance of d feet. How long does the free fall part of the ride take?

Physics A construction worker building a skyscraper accidentally drops a bolt from a height of 500 feet. Use the equation 𝑑=16 𝑡 2 to determine the time t, in seconds, that it takes the bolt to fall to the ground below.

How do you find and approximate square roots of numbers?

Ticket Out the Door Solve 𝑦 2 =676