Tag: properties and patterns of perfect squares

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Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

Having $5$ at units place, find the square of the number $185$.

  1. $34225$
  2. $48034$
  3. $15620$
  4. $83450$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$185$ $=$ $(200-15)$

$185^{2}$ $=$ $(200-15)^{2}$
$(200-15)^{2}$ $=$ $200^{2}$ $+$ $15^{2}$ $-$ $2\times200\times15$
$185^{2}$ $=$ $40000$ $+$ $225$ $-$$6000$
$185^{2}$ $=$ $34225$
Hence, Option A is correct.

Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

What is the series and also find the total of first $100$ consecutive odd numbers?

  1. $1 + 2 + 4 + 6 + 8 + 10 +... 100 = 12000$
  2. $2 + 3 + 4 + 7 + 9 + 11 +...100 = 10000$
  3. $1 + 3 + 5 + 7 + 10 + 11 +....100 = 1000$
  4. $1 + 3 + 5 + 7 + 9 + 11 +...100 = 10000$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sum of first $100$ consecutive odd numbers $= 1 + 3 + 5 + 7 + 9 + 11 + ....+100 = 10000$
Since, we know the formula for sum of consecutive odd numbers $= n^2$
So, $n = 100$, Sum $= 100^2 = 10000$

Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

Find the sum of two consecutive number for $13^2$.

  1. $84$ and $85$
  2. $83$ and $84$
  3. $86$ and $82$
  4. $81$ and $80$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the two consecutive numbers be, $\dfrac{n^{2} - 1}{2}$ and $\dfrac{n^{2} + 1}{2}$
$13^2= 169$
n = 13
$\dfrac{n^{2} - 1}{2} = \dfrac{13^{2} - 1}{2} = 84$
$\dfrac{n^{2} + 1}{2} = \dfrac{13^{2} + 1}{2} = 85$
So, the sum of two consecutive numbers = 84 + 85 = 169.

Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

$21^{2}-1$ is a product of two consecutive even numbers. Find those numbers.

  1. 21 and 22

  2. 22 and 24

  3. 20 and 22

  4. 22 and 23
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$21^{2}-1 = 400$
we can express the above number into general form $a^{2}-1 = (a + 1)\times (a - 1)$
Where a = 21
So, $21^{2}-1 = (21 + 1)\times (21 - 1)$
= $22 \times 20 = 400$
Therefore, the two even consecutive numbers are 20 and 22.