Question

Use the fact that 144 is a perfect square to evaluate StartRoot 144 EndRoot.
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Part 1
StartRoot 144 EndRootequalsStartRoot left parenthesis plus or minus nothing right parenthesis squared EndRoot

Answer 1

To evaluate \(\sqrt{144}\), we can use the fact that \(144\) is a perfect square. Specifically, \(144 = 12^2\).

Thus, we can write:

\[
\sqrt{144} = \sqrt{12^2}
\]

By the property of square roots, we have:

\[
\sqrt{a^2} = |a|
\]

So,

\[
\sqrt{12^2} = |12| = 12
\]

Therefore,

\[
\sqrt{144} = 12
\]

In part 1, as mentioned, we can express this as:

\[
\sqrt{144} = \sqrt{(12)^2}
\]

or you could also express \(144\) in terms of \((\pm 12)^2\):

\[
\sqrt{144} = \sqrt{(\pm 12)^2} = |\pm 12| = 12
\]

Thus, we confirm:

\[
\sqrt{144} = 12
\]