Intro to square-root equations & extraneous solutions 

Lessons on square-root equations

 

Radical equations 

Lesson from Math Planet on Radical Equations

 

What is the product property of square roots? 

Overview and video on the product property of square roots

 

Solving Radical Equations - Concept 

Video lesson on Radical Equations from Brightstorm website

 

Grades 9th and 10th Math 

High School math lessons for grades 9th and 10th

 

Operations on Radical Expressions 

Information on Radical Expressions

Finding Square Root:

• Above 100:

103² = 10609

Step 1. Add the number to the ones digit:
103 + 3 = 106
Step 2. Square the ones digit number (if the result is a single digit put a 0 in front of it):
3² = 09
Step 3. Place the result from Step 2 next to the result from Step 1: 10609

 

• Below 100:

97² = 9409

Step 1. Subtract the number from 100: 100- 97 = 3

Step 2. Subtract the number (from Step 1) from original number : 97-3 =94

Step 3. Square the result from Step 1 (if the result is a single digit put a 0 in front of it): 3² = 09

Step 4. Place the result from Step 3 next to the result from Step 2: 9409

 

• Below 50:

48² = 2304

Step 1. Subtract the number from 50: 50-48=2

Step 2. Subtract the result (from Step 1) from 25: 25-2 =23

Step 3. Square the result from Step 1 if the result is a single digit put a 0 in front of it ) : 2² = 04

Step 4. Place the result from Step 3 next to the result from Step 2: 2304

 

• Above 50:

53² = 2809

Step 1. Add 25 to the ones digit: 25 + 3 = 28

Step 2. Square the ones digit number ( if the result is a single digit put a 0 in front of it ) : 3² = 09

Step 3. Place the result from Step 2 next to the result from Step 1 : 2809

 

Easy Tricks to Find Square Roots and Cube Roots 

Tricks to find Square roots and cube roots

Radical Expressions & Equations

A radical expression is any expression that contains a radical symbol

 

The Square root of a number is that number that when multiplied by itself yields the original number. Every positive real number has two square roots, one positive and one negative. we use

 √  denotes the principal square root or non-negative

−√  denotes the negative square root.

The cube root of a number is that number that when multiplied by itself three times yields the original number.  denotes a cube root

Follow the following four steps to solve radical equations.

• Isolate the radical expression.
• Square both sides of the equation: Use the rule: If x = y then x² = y².
• Once the radical is removed, solve for the unknown.
• Check all answers

 

Example:

Solve .

Isolate the radical expression.

Raise both sides to the index of the radical; in this case, square both sides.

This quadratic equation now can be solved either by factoring or by applying the quadratic formula.

Applying the quadratic formula, 

Now, check the results.

If , 

If x = –5,

The solution is  or x = –5.

Product Rule of Radicals: states that the product of two or more numbers raised to a power is equal to the product of each number raised to the same power. This is same for roots. 

 

Quotient Property of Radicals: This property allows you to split the square root between the numerator and denominator of the fraction.