Question

Find the least number by which 768 should be divided to get a perfect square number. Also, find the number whose square is the resulting new number.​

Answer 1

QUESTION:-

Find the least number by which 768 should be divided to get a perfect square number. Also, find the number whose square is the resulting new number.

ANSWER:-

16

STEP BY STEP SOLUTION:-

Resolving 768 into prime factors, we get

768 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3

Clearly, by grouping the prime factors of 768 into pairs of equal factors, we are left with a factor 3, which cannot be paired.

Thus, we must divide, 768 by 3 to get a perfect square number.

New number = 768 ÷ 3 = 256

➙ 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

➙ 256 = 2² × 2² × 2² × 2²

➙ 256 = (2 x 2 x 2 x 2)²

➙ 256 = (16)²

Hence, the number whose square is the new number is 16.

Answer 2

Answer:

16

Step-by-step explanation:

find sqrt of 768 it's square root will come 27 and remainder 39 so it's perfect square would be 28 find its square and subtract that from 768