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Find the approximate square root of $$ \frac{\left(12 \frac{1}{5}\rig
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05 Apr 2025, 03:53
05 Apr 2025, 03:53
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Find the approximate square root of
$$
\(\frac{\left(12 \frac{1}{5}\right)^2-\left(5 \frac{1}{12}\right)^4}{\left(12 \frac{1}{5}\right)^2-\left(5 \frac{1}{12}\right)^2}\)
$$
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
$$
\(\frac{\left(12 \frac{1}{5}\right)^2-\left(5 \frac{1}{12}\right)^4}{\left(12 \frac{1}{5}\right)^2-\left(5 \frac{1}{12}\right)^2}\)
$$
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
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Re: Find the approximate square root of $$ \frac{\left(12 \frac{1}{5}\rig
[#permalink]
14 May 2025, 08:11
14 May 2025, 08:11
Expert Reply
Since $\(\frac{a^4-b^4}{a^2-b^2}=a^2+b^2,\left(\frac{61}{5}\right)^2+\left(\frac{61}{12}\right)^2\)$
$$
\(\begin{aligned}
& =\frac{61^2\left(12^2+5^2\right)}{5^2 \cdot 12^2}=\frac{61^2\left(12^2+5^2\right)}{5^2 \cdot 12^2} \\
& =\sqrt{\frac{61^2\left(12^2+5^2\right)}{5^2 \cdot 12^2}}=\frac{61 \times 13}{5 \times 12}=13.21 \approx 13 .
\end{aligned}\)
$$
Thus, the correct answer choice is $B$.
$$
\(\begin{aligned}
& =\frac{61^2\left(12^2+5^2\right)}{5^2 \cdot 12^2}=\frac{61^2\left(12^2+5^2\right)}{5^2 \cdot 12^2} \\
& =\sqrt{\frac{61^2\left(12^2+5^2\right)}{5^2 \cdot 12^2}}=\frac{61 \times 13}{5 \times 12}=13.21 \approx 13 .
\end{aligned}\)
$$
Thus, the correct answer choice is $B$.
gmatclubot
Re: Find the approximate square root of $$ \frac{\left(12 \frac{1}{5}\rig [#permalink]
14 May 2025, 08:11
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