The Pythagorean theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse by the formula a? + b2 = -2
If a is a rational number and b is a rational number, why could c be an irrational number?

For the value of hypotenuse can be irrational, sum of squares of other two legs might be imperfect square number.

Step-by-step explanation:

We all know, the Pythagorean theorem can be stated as follows:

The sum of squares of two legs of a right angled triangle is equal to the square of the hypotenuse.

i.e.

Where, is the hypotenuse and are the two other legs of the right angled triangle.

Given that:

and are rational numbers.

To find:

Situation for which is irrational.

Square of a rational number is always rational.

So, both will be rational.

And sum of squares of two rational numbers will also be rational.

Therefore, will also be rational.

and

For the value of can be irrational, sum of squares of other two legs might be imperfect square number.

78.59 is the mean

step-by-step explanation:

large crystals result from very slow cooling.

evaporation of water: this would produce an evaporite which is a sedimentary rock. like a salt pan in a desert. not possible to have volcanic rocks originate this way.

crystalization in molten earth: slow cooling over time. (hundreds to millions of years)

crystalization at earth's surface: this results in fast cooling. (a few hours to a few months or years)

crystalization from cooling off hot water: that would be a hydrothermal deposit. while associated with volcanics they are not volcanic rocks themselves and usually occur fairly rapidly.