Question

Simplify each expression, and classify the result as rational or irrational. HELP

Answer 1

Expressions $2\sqrt{5}-3\sqrt{5},\frac{\sqrt{42} }{\sqrt{68} } and \sqrt{7}\pi -\sqrt{14} \pi$   are irrational.

Expressions  $\frac{5\sqrt{3}-\sqrt{3} }{2\sqrt{3} }$ and $\frac{\sqrt{64} }{32}$  are rational.

Rational and irrational expression :

The given expression are,

• $2\sqrt{5} -3\sqrt{5} =\sqrt{5}(2-3)=-\sqrt{5}$

          Which is irrational.

• $\frac{\sqrt{42} }{\sqrt{68} } =\frac{\sqrt{42} }{2\sqrt{17} }$        

          Which is irrational.

• $\sqrt{5}(4\sqrt{5}-3\sqrt{5}=5$

        Which is rational.

• $\frac{5\sqrt{3}-\sqrt{3} }{2\sqrt{3} }=2$

        Which is rational.

• $\frac{\sqrt{64} }{32} =\frac{8}{32}=\frac{1}{7}$        

        Which is rational.

• $\sqrt{7} \pi -\sqrt{14}\pi =\pi (\sqrt{7}-\sqrt{14})$

         Which is irrational.

What is Rational expressions ?

• Rational expressions represent the relationship between two polynomials. It means that the numerator and denominator are both polynomials.
• It is an algebraic expression ratio with an unknown variable, similar to a fraction. We can, however, simplify this type of expression with the aid of a calculator.
• You've probably heard of rational numbers, which are written in the form p/q. In contrast, rational expressions are the ratio of two polynomials.
• To find the root or zero of a polynomial expression, we must first make it equal to zero. To find the zeros of rational functions or expressions, however, only the numerator must be set to zero after the expression has been reduced to its simplest terms.

Learn more about the rational function here:

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