What is the smallest number by which 2352 must be multiplied to get a perfect square.
Answers
What is the smallest number by which 2352 must be multiplied to get a perfect square.
ON FACTORISING 2352 WE GET
2352=2×2×2×2×7×7×3
2352=2×2×2×2×7×7×3
PAIRING THE FACTORS OF 2352=(2×2),(2×2),(7×7)
WE CAN SEE THAT THE FACTOR 3 REMAINS UNPAIRED
SO TO MAKE 2352, A PERFECT SQUARE, WE NEED A PAIR OF 3.
SO WE HAVE 2 OPTIONS,. EITHER TO DIVIDE 2352 BY 3 OR TO MULTIPLY BY 3
AS QUESTION IS GIVEN TO MULTIPLY, SO WE NEED TO MULTIPLY 3
SO THE NUMBER TO BE MULTIPLIED TO MAKE 2352 A PERFECT SQUARE IS 3
SO THE PERFECT SQUARE NUMBER IS =2352×3=7056
PERFECT SQUARE
A NUMBER IS SAID TO BE A PERFECT SQUARE IF IT HAS EVEN NUMBER OF PRIME FACTORS
EG:64,9,121 etc
FINDING SQUARE ROOT
FOR FINDING SQUARE ROOT WE FACTORISE THE NUMBER INTO PRODUCT OF PRIMES
THEN PAIR THE FACTORS AS WE DID ABOVE
THEN SELECT ONE FACTOR FROM EACH PAIR
THEN MULTIPLY THE REMAINING NUMBER
THE RESULTANT IS THE SQUARE ROOT
ANSWER
ON FACTORISING 2352 WE GET
2352=2×2×2×2×7×7×3
2352=2×2×2×2×7×7×3
PAIRING THE FACTORS OF 2352=(2×2),(2×2),(7×7)
WE CAN SEE THAT THE FACTOR 3 REMAINS UNPAIRED
SO TO MAKE 2352, A PERFECT SQUARE, WE NEED A PAIR OF 3.
SO WE HAVE 2 OPTIONS,. EITHER TO DIVIDE 2352 BY 3 OR TO MULTIPLY BY 3
AS QUESTION IS GIVEN TO MULTIPLY, SO WE NEED TO MULTIPLY 3
SO THE NUMBER TO BE MULTIPLIED TO MAKE 2352 A PERFECT SQUARE IS 3
SO THE PERFECT SQUARE NUMBER IS =2352×3=7056
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PERFECT SQUARE
A NUMBER IS SAID TO BE A PERFECT SQUARE IF IT HAS EVEN NUMBER OF PRIME FACTORS
EG:64,9,121 etc
FINDING SQUARE ROOT
FOR FINDING SQUARE ROOT WE FACTORISE THE NUMBER INTO PRODUCT OF PRIMES
THEN PAIR THE FACTORS AS WE DID ABOVE
THEN SELECT ONE FACTOR FROM EACH PAIR
THEN MULTIPLY THE REMAINING NUMBER
THE RESULTANT IS THE SQUARE ROOT