Question

2. Check if the following numbers are perfect squares.
(i) 183 (ii) 267 (iii) 484 (iv) 625​

Answer 1

Answer:

only iii) and iv) are the perfect square of 22 and 25

Answer 2

Answer:

• i) 183 ⇢ It is not a perfect square
• ii) 267 ⇢ It is not a perfect square.
• iii) 484 ⇢ It is a perfect square.
• iv) 625 ⇢ It is a perfect square.

Step-by-step explanation:

i) 183

Resolving 183 as prime factors, we get:

$\begin{array}{c|c}\underline{3}&\underline{\;183\;}\\\underline{61}&\underline{\;\;61\;\;}\\&1\end{array}$

183 = 3 × 61

As,

• 183 can't be expressed as a product of pairs of equal factors.

Therefore,

• 183 is not a perfect square.

--------------------------------------------

ii) 267

Resolving 267 as prime factors, we get:

$\begin{array}{c|c}\underline{3}&\underline{\;267\;}\\\underline{89}&\underline{\;\;89\;\;}\\&1\end{array}$

267 = 3 × 89

As,

• 267 can't be expressed as a product of pairs of equal factors.

Therefore,

• 267 is not a perfect square.

--------------------------------------------

iii) 484

Resolving 484 as prime factors, we get:

$\begin{array}{c|c}\underline{2}&\underline{\;484\;}\\\underline{2}&\underline{\;242\;}\\\underline{11}&\underline{\;121\;}\\\underline{11}&\underline{\;\;11\;\;}\\&1\end{array}$

484 = 2 × 2 × 11 × 11

As,

• 484 is the product of pairs of equal factors.

Therefore,

• 484 is a perfect square.

--------------------------------------------

iv) 625

Resolving 625 as prime factors, we get:

$\begin{array}{c|c}\underline{5}&\underline{\;625\;}\\\underline{5}&\underline{\;125\;}\\\underline{5}&\underline{\;\;25\;\;}\\\underline{5}&\underline{\;\;\;5\;\;\;}\\&1\end{array}$

625 = 5 × 5 × 5 × 5

As,

• 625 is the product of pairs of equal factors.

Therefore,

• 625 is a perfect square.