Transcript Simplifying Radical Expressions

Simplifying Radical Expressions:
• A radical expression is an expression that contains a
square root
– Ex: 57
• To be in simplest radical form, there can be no
perfect square factors (other than one) in the
radicand
2
• Perfect squares:
10
25
50
Simplify each radical expression:
− 6300
• Simplifying with variables:
𝑥2
𝑥3
𝑥4
5
𝑥
100
𝑥
101
𝑥
• Product Property of Square Roots
– Only applies to positive numbers under the square
root and zero…not negatives
− 𝟔•− 𝟐
− 𝟔• 𝟐
𝟕𝒙𝟑 • 𝟕𝒙𝟑
𝟐 𝟔•𝟒 𝟐
Square Root of a Fraction:
To be in simplest form, fractions in the numerator are
okay… but NO fractions in the denominator!
1 3
∙
2 8
1 3
∙
2 10
Geometric Mean
• The geometric mean between two numbers is the
positive square root of their product.
• For two positive numbers, a and b, the geometric
mean is represented by x in the proportion below:
𝑎 𝑥
=
𝑥 𝑏
Example
Find the geometric mean between 12 and 3
Example
48 is the geometric mean between a and b.
Find a if b=4