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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

User Imageree
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2 Answers

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Answer:

The Simplified form of
√(121) is 11, which is a rational number.

The Simplified of
√(48) is
4√(3) which is an irrational number.

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
√(121)

The above expression can be written as:


\sqrt{11^(2)}=(11^(2))^{(1)/(2)}=(11)^{(2)/(2)}=11

Hence, the Simplified of
√(121) is 11, which is a rational number.

Consider the expression
√(48)

The above expression can be written as:


√(48)=\sqrt{4^(2)*3}=4√(3)

Hence, the Simplified of
√(48) is
4√(3) which is an irrational number. Because the decimal expansion of the number is neither terminate nor periodic.

User Robin Qiu
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2 votes

Answer:

Part 1) 11 is a rational number

Part 2)
4√(3) is a irrational number

Explanation:

we know that

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

Part 1) we have


√(121)

we know that


121=11^(2)

substitute


\sqrt{11^(2)}=(11^(2))^{(1)/(2)}=(11)^{(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


√(48)

we know that


48=2^(4)(3)

substitute


\sqrt{2^(4)(3)}=(2^(4)(3))^{(1)/(2)}=4√(3)

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

User Wjohnsto
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6.6k points