Question

Find the least number by which 350 should be multiplied so as to get the perfect square. Also, find the square root of the resulting number

Answer 1

Answer:

The answer of this question is 4/350

Answer 2

Step-by-step explanation:

We have to find the smallest number by which 350 should be multiplied to get a perfect square number.

➭ The prime factorization of 350 will give us the number (or numbers) that do not have exist in pairs among the prime factors of 350.

$\Large{ \begin{array}{c|c} \tt 2 & \sf{ 350} \\ \cline{1-2} \tt 5 & \sf { 175} \\ \cline{1-2} \tt 5 & \sf{ 35} \\ \cline{1-2} \tt 7 & \sf{ 7 }\\ \cline{1-2} & \sf{ 1} \end{array}}$

350 = 2 x 5 x 5 x 7

➭ We got the numbers, 2 and 7, that do not have a pair. In order to find the perfect square number, we need to have another 2 and 7 here to make their pairs.

➭ That means we are multiplying 5² and 2 and 7 (= 350) with 14.

Thus, the least number by which 250 should be multiplied so as to get a perfect square number is 14.

➭ We also need to find the square root of the result. Back to our calculation, let's find the perfect square number.

• 350 x 14 = 4900

➭ It is easy to find the square root of 4900, since there are two zeroes at the end. We divide the number into 2 parts- 49 and 00.

• Square root of 49 = 7
• 00 = 0

Thus, the square root of 4900 is 70.

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