Check the solution to "In the following, simplify using absolute values as..."

David Lewis

Answered question

2021-12-06

In the following, simplify using absolute values as necessary.

\sqrt{144 x^{2} y^{2}}

Joseph Fair

Beginner2021-12-07Added 34 answers

Given information: Asquare root is given as

\sqrt{144 x^{2} y^{2}}

.
Calculations: We have been given an expression is

\sqrt{144 x^{2} y^{2}}

.
To find the odd and even roots by using the absolute value as necessary, we are use power property of exponent i.e.

{(a^{m})}^{n} = a^{m \cdot n}

as shown below:

\Rightarrow \sqrt{144 x^{2} y^{2}}

[Simplify the square root of

144 x^{2} y^{2}

]

\Rightarrow \sqrt{{(12 x y)}^{2}}

[Break the power exponent in the form of

{(a^{m})}^{n} = a^{m \cdot n}

]

\Rightarrow 12 | x y |

[

\sqrt{n} {a^{n}} = | a |

, if the value of n is even.]
Thus, index of

\sqrt{144 x^{2} y^{2}}

is even.
Hence, the simplification

\sqrt{144 x^{2} y^{2}} i s 12 | x y |

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