Question

which of the following values for n makes the inequality √2n < 5 true?
a 8
b 12.5
c 16
d 18

Answer 1

To solve the inequality \( \sqrt{2n} < 5 \), we can first square both sides (assuming \( n \) is non-negative, since we're dealing with a square root):

\[
2n < 25
\]

Now, divide both sides by 2:

\[
n < 12.5
\]

Now we can evaluate the given options:

a) \( n = 8 \): \( 8 < 12.5 \) (True)

b) \( n = 12.5 \): \( 12.5 < 12.5 \) (False)

c) \( n = 16 \): \( 16 < 12.5 \) (False)

d) \( n = 18 \): \( 18 < 12.5 \) (False)

The only value of \( n \) that satisfies the inequality \( \sqrt{2n} < 5 \) is:

**a) 8**