Question

If Joelle multiplied $792$ by a positive integer and came up with a perfect square as her answer, then what is the smallest integer she could have multiplied $792$ by

Answer 1

Answer:

22

Step-by-step explanation:

In mathematics a perfect square number is one whose square root results in a natural number.

Example:

$\sqrt{4}=2\\ \sqrt{9} = 3$

To solve this problem we can do:

$\sqrt{792}$

By properties of roots ...

$\sqrt{792} = \sqrt{6*132}$

$= \sqrt{6 * 6 * 22} =\sqrt{6 ^ 2 * 22}$

$= 6\sqrt{22}$

So, so that the multiplication of 792 by an integer becomes a perfect square, you have to multiply it by 22 to make $22 ^ 2$ and thus "eliminate" the root.

792 * 22 = 17424

You can verify that 17424 is a perfect square since root (17424) = 132 and 132 is a natural number