Question
Show that 500 is not a perfect square.
✓
Answer
We have, $500=\underline{2 \times 2} \times \underline{5 \times 5} \times 5$
Here, by grouping into a pair of equal factors, we are left with one factor 5, which cannot be paired.
Hence, 500 is not a perfect square.
| 2 | 500 |
| 2 | 250 |
| 5 | 125 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Hence, 500 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.
Explore more
Similar questions
Rashmi has a road map with a scale of 1 cm representing 18 km . She drives on a road for 72 km . What would be her distance covered In the map?
Show that: $\frac{\sqrt[3]{-512}}{\sqrt[3]{343}}=\sqrt[3]{\frac{-512}{343}}$
→Consider the following pattern
$\begin{array}{l}2^3-1^3=1+2 \times 1 \times 3,3^3-2^3=1+3 \times 2 \times 3 \\4^3-3^3=1+4 \times 3 \times 3\end{array}$
Using the above pattern, find the value of the following:
(i) $7^3-6^3$$\qquad\quad$(ii) $12^3-11^3$
(iii) $20^3-19^3$$\quad~~$(iv) $51^3-50^3$
→$\begin{array}{l}2^3-1^3=1+2 \times 1 \times 3,3^3-2^3=1+3 \times 2 \times 3 \\4^3-3^3=1+4 \times 3 \times 3\end{array}$
Using the above pattern, find the value of the following:
(i) $7^3-6^3$$\qquad\quad$(ii) $12^3-11^3$
(iii) $20^3-19^3$$\quad~~$(iv) $51^3-50^3$
Find the smallest number by which the given number must be divided so that the resulting number is a perfect square: $1800$
→The sum of the radius of the base and height of a solid cylinder is $37\ m.$ If the total surface area of the solid cylinder is $1628\ m^2$, find the circumference of its base.
→Solve: $\frac{4\text{x}+7}{9-3\text{x}}=\frac{1}{4}$
→If $\Big(\text{x}+\frac{1}{\text{x}}\Big)=4$ Find the values of: $\Big(\text{x}^2+\frac{1}{\text{x}^2}\Big)$
→A student used the proportion $\frac{\text n}{100}=\frac{5}{32}$ to find $5 \%$ of 32. What did the student do wrong?
→In a stack there are $5$ books each of thickness $20 mm$ and $5$ paper sheets each of thickness $0.016 mm$. What is the total thickness of the stack?
→In the below figure both $RISK$ and $CLUE$ are parallelograms. Find the values of $x.$
→