Download App

Squares and Square Roots — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsSquares and Square Roots2 Marks
Question
Using prime factorization method, find the following numbers are perfect squares?
2048
✓

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.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Mark Question" from Squares and Square Roots→Squares and Square Roots — all question types→Maths STD 8 question papers→Maharashtra Board STD 8 question papers→Maharashtra Board question paper generator→

Similar questions

Express the following as a rational number of the form $\frac{\text{p}}{\text{q}}:$
$\frac{6}{7}+1+\frac{-7}{9}+\frac{19}{21}+\frac{-12}{7}$
→
Express $\frac{-3}{5}$ as a rational number with denominator.
-40
→
Factorize of the following expressions:
2ax + bx + 2ay + by
→
Write down the number of faces of the following figures:
Cuboid.
→
$\frac{15}{12}, \frac{7}{16}$
→
Find the following products:
$\left(x^2-5 x+8\right) \times\left(x^2+2\right)$
→
Write the following numbers in standard form:
0.0027
→
Subtract the first rational number from the second in the following:
$\frac{3}{8},\frac{5}{8}$
→
Find the following products:
$ \big(\text{p}^2 + 16\big) \big(\text{p}^2−\frac{1}{4}\big)$
→
Factorize of the following expressions:
$x a^2+x b^2-y a^2-y b^2$
→