Directions: What could the lengths of the legs be such that the lengths are integers and *x * is an irrational number between 5 and 7?

### Hint

What is a wrong answer? How can you use this wrong answer to move towards an answer?

What does it mean to be irrational between 5 and 7?

### Answer

Here are the lengths of the legs

3 and 5,

3 and 6,

4 and 4,

4 and 5,

2 and 5,

2 and 6,

1 and 5,

1 and 6

3 and 5,

3 and 6,

4 and 4,

4 and 5,

2 and 5,

2 and 6,

1 and 5,

1 and 6

Source: Daniel Luevanos

I said 3 and 4

Which Pair is it??

Can someone help me out with how 6 and 2 & 6 and 1 are solutions?

6^2 + 2^2 = 36 + 4 = 40. The sqrt of 40 is not an irrational number (it ends) = 6.32455532.

Also, 6^2 + 1^2 = 36 + 1 = 37. The sqrt of 37 is not an irrational number = 6.08276253.

Both numbers end, therefore are not irrational.

Just because the decimal ends on your calculator does not mean that it actually ends. The calculator will only show a certain number of digits on your screen.

Sqrt(40) is irrational because 40 is not a perfect square. The decimal places will keep going and will never repeat a sequence, so therefore it is irrational.

Only perfect squares are rational. sqrt(25) = 5

A calculator provides a rounded decimal because it must. It would not be possible to list the infinite number of digits for irrational numbers, so it must be approximated when represented in decimal form.