Question

Given that 1.4 < √2 < 1.5, find the corresponding range for the value of each expression. 2-√2

Answer 1

To find the corresponding range for the value of the expression 2 - √2, we can subtract the square root of 2 from both sides of the given inequality.

1.4 - √2 < √2 - √2 < 1.5 - √2

Simplifying the middle term, we have:

1.4 - √2 < 0 < 1.5 - √2

Therefore, the corresponding range for the expression 2 - √2 is:

1.4 - √2 < 2 - √2 < 1.5 - √2

Answer 2

Based on the given information that 1.4 < √2 < 1.5, we can find the corresponding range for the expression 2 - √2.

Substituting the upper and lower bounds of the range for √2, we get:

2 - 1.5 < 2 - √2 < 2 - 1.4

0.5 < 2 - √2 < 0.6

Therefore, the corresponding range for the expression 2 - √2 is 0.5 to 0.6.