nwbgamer
contestada

Simplify each square root expression. Describe the simplified form of the expression as rational or irrational. In your final answer, include all of your work. √121 √48

Respuesta :

calculista

Answer:

Part 1) 11 is a rational number

Part 2) [tex]4\sqrt{3}[/tex] is a irrational number

Step-by-step explanation:

we know that

A Rational Number is a number that can be made by dividing two integers

Part 1) we have

[tex]\sqrt{121}[/tex]

we know that

[tex]121=11^{2}[/tex]

substitute

[tex]\sqrt{11^{2}}=(11^{2})^{\frac{1}{2}}=(11)^{\frac{2}{2}}=11[/tex]

Is a rational number, because i can express the number 11 as the ratio of two integers (as example 11/1)

Part 2) we have

[tex]\sqrt{48}[/tex]

we know that

[tex]48=2^{4}(3)[/tex]

substitute

[tex]\sqrt{2^{4}(3)}=(2^{4}(3))^{\frac{1}{2}}=4\sqrt{3}[/tex]

Is a irrational number, because cannot be expressed as the ratio of two integers

Answer:

The Simplified form of [tex]\sqrt{121}[/tex] is 11, which is a rational number.

The Simplified of [tex]\sqrt{48}[/tex] is [tex]4\sqrt{3}[/tex] which is an irrational number.

Step-by-step explanation:

Consider the provided root expression.

Irrational   number: A   number is irrational if it cannot   be   expressed by dividing two     integers. The decimal expansion of     Irrational numbers are neither terminate nor     periodic.

Consider the expression [tex]\sqrt{121}[/tex]

The above expression can be written as:

[tex]\sqrt{11^{2}}=(11^{2})^{\frac{1}{2}}=(11)^{\frac{2}{2}}=11[/tex]

Hence, the Simplified of [tex]\sqrt{121}[/tex] is 11, which is a rational number.

Consider the expression [tex]\sqrt{48}[/tex]

The above expression can be written as:

[tex]\sqrt{48}=\sqrt{4^{2}\times3}=4\sqrt{3}[/tex]

Hence, the Simplified  of [tex]\sqrt{48}[/tex] is [tex]4\sqrt{3}[/tex] which is an irrational number. Because the decimal expansion of the number is neither terminate nor     periodic.

Otras preguntas