Radicals and Rationals

Write as a radical.

• a

• b

• c

• d

• A
• B
• C
• D

• x = 6, x = -1

• x = -6, x = 1

• x = 1

• x = 6

• a
• b
• c
• d

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.

• x = -6
• x = 3
• x = -3
• x = 5±

Solve the radical equation. Don't forget to check your answers!

• x = -6

• x = 3

• x = 7/3

• x = -5

• x = 49
• x = 53
• x = 45
• x = 18

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