Question

using prime factorisation,state which of the following is /are perfect square? a) 289 b)445​

Answer 1

Step-by-step explanation:

Prime Factorization of 289 ⟹289 = 17x17. Since, 17 is a prime number we can't write further factors of 17. Since 17 occurs two times in the factor of 289, taking both the factors common as one, we get 289 is a perfect square number, and 17 is the perfect square of the given number 289.

2) 445

No, the number 445 is not a perfect square.

Answer 2

Answer a :-

• 289 is a perfect square.

To find :-

• Whether 289 is a perfect square.

Solution :-

• Let's find whether 289 is a perfect square or not using prime factorisation method!

Prime factorisation of 289 :-

$\begin{array}{c | c} \underline{17}&\underline{289} \\ \underline{17}&\underline{17} \\ &1\end{array}$

The given number is 289.

It can be expressed as :-

$289 = \underbrace{17 \times 17}$

Since :-

• 289 can be expressed as the product of pairs of equal prime factors.

Hence, 289 is a perfect square.

Answer b :-

• 445 is not a perfect square.

To find :-

• Whether 445 is a perfect square.

Solution :-

• Let's find whether 445 is a perfect square or not using prime factorisation method!

Prime factorisation of 445 :-

$\begin{array}{c | c} \underline{5}& \underline{445} \\\underline{89}&\underline{89} \\ &1\end{array}$

The given number is 445.

It can be expressed as :-

$445 = 5 \times 89$

Since :-

• 445 cannot be expressed as the product of pairs of equal prime factors.

Hence, 445 is not a perfect square.

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