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Squares and Square Roots — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSSquares and Square Roots2 Marks
Question
Using prime factorization method, find the following numbers are perfect squares$? 2048$
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Answer

$2048 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2$
$\begin{array}{c|c} 2& 2048 \\ \hline 2 & 1024 \\\hline 2&512 \\\hline 2&256 \\\hline 2&128 \\\hline 2&64 \\\hline 2&32 \\\hline2&16 \\\hline2&8 \\\hline2&4 \\\hline2&2 \\\hline&1 \end{array}$
Grouping them into pairs of equal factors, $2048 = (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × 2$
The last factor, $2$ cannot be paired.
Hence, $2048$ is not a perfect square.

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