Question

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

Answer 1

Answer:

The Simplified form of $\sqrt{121}$ is 11, which is a rational number.

The Simplified of $\sqrt{48}$ is $4\sqrt{3}$ 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 $\sqrt{121}$

The above expression can be written as:

$\sqrt{11^{2}}=(11^{2})^{\frac{1}{2}}=(11)^{\frac{2}{2}}=11$

Hence, the Simplified of $\sqrt{121}$ is 11, which is a rational number.

Consider the expression $\sqrt{48}$

The above expression can be written as:

$\sqrt{48}=\sqrt{4^{2}\times3}=4\sqrt{3}$

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

Answer 2

Answer:

Part 1) 11 is a rational number

Part 2) $4\sqrt{3}$ 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

$\sqrt{121}$

we know that

$121=11^{2}$

substitute

$\sqrt{11^{2}}=(11^{2})^{\frac{1}{2}}=(11)^{\frac{2}{2}}=11$

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

$\sqrt{48}$

we know that

$48=2^{4}(3)$

substitute

$\sqrt{2^{4}(3)}=(2^{4}(3))^{\frac{1}{2}}=4\sqrt{3}$

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