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Find the two numbers which on multiplication with √360 gives a rational number. Are these numbers rational or irrational? Please explain in detail it is urgent 50 points.

User Gadolf
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To find the two numbers that, when multiplied by the square root of 360, give a rational number, we can start by expressing 360 as a product of its prime factors:

360 = 2^3 * 3^2 * 5

Then, we can take the square root of 360:

√360 = √(2^3 * 3^2 * 5) = 2 * 3 * √5

Now, we can see that if we multiply 2 or 3 by √360, we will get a rational number because both 2 and 3 are rational numbers. On the other hand, if we multiply √5 by √360, we will get an irrational number because √5 is an irrational number.

Therefore, the two numbers that, when multiplied by √360, give a rational number are 2 and 3. These numbers are rational.
User Squiguy
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