Radical Operations

Simplify the following radical: √32

• 3√2

• 4√8

• 16√2

• 4√2

√45

• 3√5

• 5√3

• 9√5

• 5√9

Simplify

• A

• B

• C

• D

√5

• 11√5

• 11√10

• 5√5

• 12√10

Is the result rational or irrational? Explain.

• Rational; The sum of two rationals is always rational.

• Irrational; The sum of a rational and an irrational is always irrational.

• Rational; The product of two rationals is always rational.

• Irrational; The product of a nonzero rational and an irrational is always irrational.

Is the result rational or irrational? Explain.

• Rational; The sum of two rationals is always rational.

• Irrational; The sum of a rational and an irrational is always irrational.

• Rational; The product of two rationals is always rational.

• Irrational; The product of a nonzero rational and an irrational is always irrational.

Is the result rational or irrational? Explain.

• Rational; The sum of two rationals is always rational.

• Irrational; The sum of a rational and an irrational is always irrational.

• Rational; The product of two rationals is always rational.

• Irrational; The product of a nonzero rational and an irrational is always irrational.

Is the result rational or irrational? Explain.

• Rational; The sum of two rationals is always rational.

• Sometimes rational, sometimes irrational; The sum of two irrationals is sometimes rational, sometimes irrational.

• Rational; The product of two rationals is always rational.

• Sometimes rational, sometimes irrational; The product of two irrationals is sometimes rational, sometimes irrational

Q1. What is the value of the expression?

• 13√3

• 10√30

• 13√6

• 11√3

Simplify:
6√2 ⋅5√14

• 32√7

• 60√7

• 2√7

• 30√7