Question

11. Examine if each of the following is a perfect square:

(ii) 190
(iii) 841
step by step please in prime factorisation method​

Answer 1

Step-by-step explanation:

Given 11. Examine if each of the following is a perfect square:(ii) 190(iii) 841 step by step please in prime

Now we need to find the given numbers are perfect squares by prime factorization method.

So first number will be 190 Taking out the factors we get

190 = 2 x 5 x 19  

So 190 is not a perfect square.  

Now proceeding with the second number we get

841 = 29 x 29.  

So 841 is a perfect square.  

# BAL

Answer 2

Answer:

i) 190 = 2 × 5 × 19 - since we don't have a prime factor occurring an even number of times, this is not a perfect square.

ii) 841 = 29 × 29 - 29 occurs an even number of times. So, 841 is a perfect square.

Step-by-step explanation:

A perfect square is number that can be expressed as a product of two equal integers.

A perfect square has each distinct prime factor occurring an even number of times.

Now, using prime factorization, let's examine whether the two numbers are perfect squares.

i) 190 = 2 × 5 × 19 - since we don't have a prime factor occurring an even number of times, this is not a perfect square.

ii) 841 = 29 × 29 - 29 occurs an even number of times. So, 841 is a perfect square.