Example Question - negative square root
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Solving an Inequality with Negative Square Root
The image shows an inequality with two empty boxes on either side of the negative square root of 71. To solve this, we need to find two numbers that are less than and greater than the negated square root of 71. Recall that taking the square root of a positive number results in a positive number and when we add a negative sign to it, it makes the expression negative. The square root of 71 is approximately 8.43 (since √64 = 8 and √81 = 9, and 71 is between 64 and 81). Therefore, -√71 is approximately -8.43 Since we need a number less than -8.43 and a number greater than -8.43, we could choose integers for simplicity. For the first box, let's choose -9 because -9 is less than -8.43. For the second box, we could choose -8 because -8 is greater than -8.43. So, in "en" language code, the inequality would be filled in as: -9 < -√71 < -8
Solving Inequality with Negative Square Root
The image shows an inequality with a square root and two empty boxes for numbers. The inequality is as follows: \[ \text{[Box 1]} < -\sqrt{118} < \text{[Box 2]} \] To solve this, let's find the square root of \( 118 \): The square root of \( 118 \) is an irrational number, and it is approximately equal to \( 10.86278 \) when we take the positive root. However, in this context, we're looking at the negative square root of \( 118 \), which would be approximately \( -10.86278 \). Now, we're looking for two integers that the negative square root of \( 118 \) falls between. Since \( -10.86278 \) is between \( -11 \) and \( -10 \), these would be the integers we are looking for: \[ -11 < -\sqrt{118} < -10 \] So, the numbers that should fill the boxes from left to right are \( -11 \) and \( -10 \).
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