### Concept (1)

When simplifying square roots, we give the positive and negative answer if solving an equation that did not originally have a square root. Otherwise, we give only the principal root. Square roots of negative numbers have non-real answers, which is why square roots of variables sometimes include the condition that the variable is greater than zero. Knowledge of math radicals is important when solving quadratic equation problems.

### Sample Problems (8)

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Simplify:

32x⁴
given x > 0
###### Problem 1
How to simplify a simple square root statement.

Simplify:

75³y⁸z⁵
given x,y,z > 0
###### Problem 2
How to simplify a square root statement with multiple components.

Simplify:

64x³y⁷z⁵
given x,y,z > 0
###### Problem 3
How to simplify a cube root statement with multiple components.

Simplify:

36⁄49
-8⁄125
3⁄25
###### Problem 4
How to simplify the root of a fraction.
###### Problem 5
Exploring the placement of a negative in radical expressions.
###### Problem 6
Simplifying roots of fractions and decimals.
###### Problem 7
Simplifying radicals using a factor tree.
###### Problem 8
Using perfect squares and cubes to simplify radicals.