Question

using the prime factorization method find which of the following numbers are perfect squares 1) 189,225,2048,343,2916,11025,3549​

Answer 1

Answer:

1)189 - not a perfect square

2)225- perfect square

3)2048- not a perfect square

4)343- not a perfect square

5)2916-perfect square

6)11025-perfect square

7)3549- not a perfect square

Step-by-step explanation:

Let N be a number

Using prime factorization method, calculate the total number of factors of the given number

      ;

where a ,b and c are prime factors of number N and p,q and r are the power raised of the prime factors respectively.

Total number of factors = n =

1)189

189 = 3×3×3×7=      ;

n = (3+1)(1+1) = 8 = not a odd number

Hence 189 is not a perfect square.

2)225

225=        ;

n = (2+1)(2+1) = 9 = odd number

hence 225 is a perfect square =  

3) 2048

2048 =     ;

n = 11+1 = 12= not a odd number  

hence 2048 is not a perfect square.

4)343

343 =      ;

n = 3+1 = 4

not a odd number hence 343 is not a perfect square.

5)2916

2916=      ;

n=

odd number , Hence 2916 is a perfect square

6)11025

11025=      ;

n = which is a odd number

therefore 11025 is a perfect square =  

7)3549

3549=    ;

n = (1+1)(2+1)(3+1)=24 which is a even number hence 3549 is not a perfect square.