Name:______Notes
2.5 Square Roots
Numbers such as 1, 4, 9, 16, and 25 are called ______, because they are squares of ______.
A ______of a number is one of its two equal factors.
4 · 4 = 16, so 4 is the ______of 16.
The symbol ,called a ______, is used to show a ______square root.
Find each square root. Think…what times itself gives you 81? (? · ? = 81)
Every positive number has TWO square roots: positive and negative.
The symbol for negative square root is:
shows the ______square root of 25.
Since (–5)² = 25, then = –5
shows both ______and ______square root of 25.
= 5 and –5
If n² = a, then n =
c² = 9b² = 169 m² = 289
c = b =m =
c =b =m =
To place 25 chairs in a square arrangement, how many chairs should be in each row?
Moesha has 196 pepper plants that she wants to plant in square formation. How many pepper plants should she plant in each row?
A new restaurant has ordered 64 tables for its outdoor patio. If the manager arranges the tables in a square formation, how many will be in each row?
Area of a square is equal to the square of the length of a side. A = s²
A miniature portrait of George Washington is square and has an area of 169 square centimeters. How long is each side of the portrait?
The formula for the perimeter of a square is P = 4s, where s is the length of a side. Find the perimeter of each square.
What is ? Think…what times itself gives you –25? (? · ? = –25) ______
Find each square root.
1. 2. 3. 4.
5. 6. 7. 8.
Solve each equation
d² = 64x² = 121 n² = 169
What if it is not a perfect square?
The square root of a number that is not a perfect square falls between two ______whole numbers.
Step 1Determine whether a number is a perfect square.
- Is the number 29 a perfect square? Is there a whole number which can be squared to equal 29? _____
Step 2Find the two consecutive whole numbers between which the lies.
- The number 25 is the closest perfect square ______than 29. What is ? _____
- The number 36 is closest perfect square greater than 29. What is ? _____
- lies between and . What are the two consecutive whole numbers between which lies? ______
Find the two consecutive whole numbers between which the square root of a given number lies.
Then circle the nearest integer.
______ ______ ______
______ ______ ______
***Under what condition is ?
Spiral Review
1) The radius of the Sun is 6.96 meters. Write this distance in standard form.
Write each expression using exponents
2) 6 · 6 · 63) 2 · 3 · 3 · 2 · 2 · 24)
5) What is absolute value of -18?6) Find
7) 8 – 2(5) =8) (–2)(3)(–5) =
Using the numbers 2, 3, and 4, write an example of the
9) Associative Property of Multiplication ______; 10) Distributive Property ______
HOMEWORK 2.5
1. Find each square root
2. Solve each equation
d² = 400x² = 289 n² = 121
3. Find the two consecutive whole numbers between which the square root of a given number lies.
Then circle the nearest integer.
______ ______ ______
______ ______ ______
4. Compare the following numbers using <, >, or = .
15 _____ _____
502% ______ 11² ______1.21
5. Order the following numbers in ascending order.
1.5 , 15%, ,
6. A marching band wants to form a square in the middle of the field. If there are 225 members in the band, how many should be in each row?
7. If the area of a square is 529 square inches, what is the length of a side of the square?