what is the smallest natural number by which 1792 should be multiplied

1.	what is the smallest natural number by which 1792 should be multiplied so that it becomes a perfect square? method please answer
Answer» Answer: By using prime factorization METHOD we get 1792=2×2×2×2×2×2×2×2×7 1792=(2^8)×7 SQUARE root on both sides √1792=(2^4)×√7 to MAKE it a PERFECT square we need even no. of sevens multiplied (i.e even power on 7) we have only 7^1 the nearest even power would be 7^2 1 more seven MUST be multiplied to make 7^1 to 7^2 ∴7 must be multiplied to 1792 to make it a perfect square. so, one

what is the smallest natural number by which 1792 should be multiplied so that it becomes a perfect square? method please answer

Answer»

Answer:

By using prime factorization METHOD we get

1792=2×2×2×2×2×2×2×2×7

1792=(2^8)×7

SQUARE root on both sides

√1792=(2^4)×√7

to MAKE it a PERFECT square we need even no. of sevens multiplied

(i.e even power on 7)

we have only 7^1

the nearest even power would be 7^2

1 more seven MUST be multiplied to make 7^1 to 7^2

∴7 must be multiplied to 1792 to make it a perfect square.

so, one