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Question

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

x=299
, y=301
x equals 299 , y equals 301

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

x=100
, y=400

Answer 1

To solve the inequality \( \sqrt{x} < \sqrt{300} < \sqrt{y} \), we first need to approximate \(\sqrt{300}\).

Calculating \(\sqrt{300} \approx 17.32\). This helps us determine the values for \(x\) and \(y\) that satisfy the inequality.

1. Finding \(x\): We need \( \sqrt{x} < \sqrt{300} \), which simplifies to: \[ x < 300 \] We seek the largest perfect square less than 300, which is \(256\) (since \(16^2 = 256\) and \(17^2 = 289\), but \(289 > 300\)).

2. Finding \(y\): We need \( \sqrt{300} < \sqrt{y} \), which simplifies to: \[ y > 300 \] We seek the smallest perfect square greater than 300, which is \(361\) (since \(19^2 = 361\) and \(18^2 = 324\), but \(324 < 300\)).

Thus, the correct values are \(x = 256\) and \(y = 361\).

Therefore, the correct response is: x equals 256, y equals 361.