Rational and Radical Review

Simplify the following expression:

• 5

• 25

• 125

• 625

Simplify

• x²y√xy

• xy

• x²y²

• Can't Simplify

√3

• 7√3

• Can't Simplify

• 6√15

• 6√3

Write the above expression in exponential form.

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• 
• 
• 

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

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.

• 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.