Simplifying Radical Expressions in Pre-Algebra

Professor Von Schmohawk explains how roots can be expressed as radical or exponential expressions and emphasizes simplifying them to their simplest forms. The video covers methods to simplify radical expressions, including factoring numbers under radical signs and using exponents. It also discusses simplifying expressions with variables, highlighting the importance of absolute values for even roots. The video concludes with examples of simplifying cube roots and introduces the concept of irrational numbers.

What is the square root of 81?

• 18

• 9

• 8

• 81

Why might a farmer prefer using numbers over radical expressions for dimensions?

• Numbers represent irrational roots better.

• Radical expressions are easier to calculate.

• Radical expressions are too precise.

• Numbers are simpler for practical measurements.

How can the square root of 50 be simplified?

• 10

• Square root of 25 plus square root of 2

• 25 times the square root of 2

• 5 times the square root of 2

What is the simplified form of the square root of 300?

• 15 times the square root of 2

• 10 times the square root of 3

• Square root of 3 times square root of 100

• 30

How do you simplify the square root of 3675?

• 35 times the square root of 3

• 60 times the square root of 3

• Square root of 3 times square root of 1225

• 3675

What results from dividing the square root of 3675 by the square root of 300?

• 5 quarters

• 35 tenths

• 7 halves

• 70 halves

Why must variables under a square root sign be written as absolute values?

• To make it easier to factor

• To represent irrational numbers

• To simplify the calculation

• To ensure the result is always positive

How is the cube root of 72 simplified?

• 6 times the cube root of 2

• 3 times the cube root of 8

• 72

• 2 times the cube root of 9

What is the simplified form of the square root of 72?

• 72

• Square root of 36 times square root of 2

• 8 times the square root of 9

• 6 times the square root of 2

Why can't most roots be represented by integers or rational numbers?

• They are always negative.

• They are too complex to calculate.

• They are irrational numbers.

• They can only be expressed as radicals.