Question

Determine the perfect square values that best complete the expression x−−√<300−−−√<y√
by squeezing the interval on a number line.(1 point)
Responses

x=289
, y=324
x equals 289 , y equals 324

x=100
, y=400
x equals 100 , y equals 400

x=256
, y=361
x equals 256 , y equals 361

x=299
, y=301

Answer 1

To analyze the expression \(\sqrt{x} < \sqrt{300} < \sqrt{y}\), we need to calculate \(\sqrt{300}\) and identify the perfect squares that surround it on the number line.

First, we find the approximate value of \(\sqrt{300}\):

\[
\sqrt{300} \approx 17.32
\]

Next, we determine the perfect squares immediately below and above this value:

1. The perfect square just below \(\sqrt{300}\) is \(\sqrt{289} = 17\) (since \(17^2 = 289\)).
2. The perfect square just above \(\sqrt{300}\) is \(\sqrt{324} = 18\) (since \(18^2 = 324\)).

Thus, we satisfy the condition \(\sqrt{x} < \sqrt{300} < \sqrt{y}\) with \(x = 289\) and \(y = 324\).

Considering the response options given:

- \(x = 289, y = 324\)
- \(x = 100, y = 400\)
- \(x = 256, y = 361\)
- \(x = 299, y = 301\)

The correct option is:

**x equals 289, y equals 324**.