Question

Using prime factorization examine which of the following numbers are perfect square 1458​

Answer 1

Answer:(3^6) * 2

Step-by-step explanation:

1458 = 729*2 = (9^3)*2 = ((3^2)^3)*2 = (3^6)*2

Answer 2

POINTS TO NOTICE:-

1. FOR QUESTION RELATED TO SOLVING PROBLEMS ON PRIME FACTORIZATION
2. TAKE THE COLUMN METHOD TO SOLVE IT AS A PRIMARY TASK
3. TAKE THE NO. AND SOLVE IT BY DIVIDING IT WITH THE SMALLEST DIVISIBLE NUMBER
4. TAKE ON DIVISION UNTIL YOU GET 1 OR A PRIME NO.

GIVEN:

PRIME FACTORIZATION METHOD

TO FIND:-

TO CHECK EITHER 1458 IS A PERFECT SQUARE

SOLUTION:-

CHECK BY DIVIDING IT BY 2

2|1458

3| 729

3| 243

3 | 81

3 | 27

3 | 9

3 | 3

1 | 1

SO YOU SEE , 1458 = 2 × 3 × 3 × 3 × 3 × 3 × 3 × 1

THAT IS FOR PERFECT SQUARE IF YOU MAKE PAIRS THEN 3 HAS 3 PAIRS BUT IT IS NOT VALID FOR NO. 2

HENCE IT IS NOT A PERFECT SQUARE

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