Question

find the value of k such that 156k is a perfect square​

Answer 1

Final Answer:

The correct value of k is the positive integer 39 to make the number 156k a perfect square.

Given:

The number 156k, where k is assumed to be a positive integer.

To Find:

We are required to find the value of k.

Explanation:

A perfect square is such a number which can be split into two equal integers.

On the other hand, if we multiply one integer with itself once, we get the perfect square.

Step 1 of 3

Factorize the number 156k into its constituents factors in the following way.

$156k=2 *2*3*13*k=2^2*3*13*k$

Step 2 of 3

It is evident from the above factorization, that only the factor 2 appears in square form.

To make the number 156k a perfect square, we should assign the following value to k.

$k=3*13=39$

Step 3 of 3

Thus, on putting the value of k=39, we get the following perfect square.

$2 *2*3*13*k\\=2^2*3*13*39\\=6084\\=78^2$

Therefore, the required value of k is equal to 39 to make the number 156k a perfect square.

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