Warm Up
1. The number that tells how many times the base of a power is used
as a factor is called the _____________.
2. −3 + −4 − (−8)
3. −(−4)3
4. 𝑎3 𝑥 4 𝑥 8 𝑎4 𝑧 4
5.
2
−
6
÷
3
−
8
Lesson 13: Calculating and
Comparing Square Roots
Expressions and Equations
Vocabulary
• Perfect square: a number that is the square of an integer
• Radicand: the number or expression under a radical symbol
• Square root of 𝑥: the number whose square is 𝑥, denoted
𝑥
Example 1: Finding Square roots of Perfect
Squares
A. Is the radicand in 50 a perfect square? Explain.
B. Is the radicand in 64 a perfect square? Explain.
Simplifying Square Roots
• Not all numbers are square roots, but we can use our knowledge of
perfect squares to estimate their values.
• Radicals fall under exponents in the order of operations because
radicals can be written using fractional exponents.
Example 2: Estimating Square Roots
Estimate the value of 50 to the nearest integer. Explain your
reasoning.
Example 3: Comparing Expressions Involving
Square Roots
Compare the expressions.
4 + 36
9 + 25
An Important Note
• Note that 𝟒 + 𝟑𝟔 ≠ 𝟒 + 𝟑𝟔
Example 4: Ballroom Dancing
• The area of a dance floor in the shape of a square is 289 square feet.
What is the side length of the dance floor?