Does a positive integer times a positive integer equal a positive integer?

Mathematics

2 answers:

elixir [45]3 years ago

8 0

Yes it will always be positive

hodyreva [135]3 years ago

7 0

Answer:

Yes, two positive real numbers will always equal a positive number. If two numbers have the same sign, whether positive or negative, the product will always be positive.

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3 years ago

The figure is a square. Find the length of side x in simplest radical form with a rational denominator.

nika2105 [10]

Answer:

$10\sqrt{2}$

Step-by-step explanation:

The diagonal of any square with side length $s$ is equal to $s\sqrt{2}$ . Since the side length of the square is 10, the diagonal must be $\boxed{10\sqrt{2}}$ .

To support and prove this:

The diagonal creates two 45-45-90 triangles, with the diagonal being the hypotenuse of both of these triangles. The Pythagorean Theorem states that in any triangle, the sum of the squares of both legs is equal to the square of the hypotenuse ( $a^2+b^2=c^2$ ).

Call the diagonal $d$ . In these two triangles, both legs are equal to 10 (the side lengths of the square), and the hypotenuse is the diagonal. Thus, we have: