Question

find the smallest number by which 2335 must be multiplied to het a perfect square.Also find the square root of the new number..
Please help?!!!​

Answer 1

Step-by-step explanation:

Given that: Find the smallest number by which 2335 must be multiplied to get a perfect square.Also find the square root of the new number.

Solution: To find that number,one can do prime factorisation of 2335

$2335 = 5 \times 467$

Here we can see that,both the prime factors appears only once,so one have to multiply 2335 by 5 and 467,i.e. 2335 itself.

Thus,the smallest number which when multiplied by 2335 gives a perfect square is 2335.

$2335 \times 2335 = 5 \times 467 \times 5 \times 467 \\ \\ {(2335)}^{2} = {5}^{2} \times {(467)}^{2}$

Thus,the square root of new number is 2335.

Hope it helps you.