Example Question - square root approximation
Here are examples of questions we've helped users solve.
Completing Inequality with Approximate Value
The image shows an incomplete inequality, where the middle term is "-√122", and there are inequality signs facing outwards on either side. To complete the inequality meaningfully, we should consider the value of "-√122". First, we calculate the square root of 122. Since 122 is not a perfect square, its square root will be irrational and can't be simplified into an exact integer or simple fraction. However, we can approximate this value. √122 ≈ 11.04536 Now we take the negative of this value to match the term in the inequality: -√122 ≈ -11.04536 So, the center term of the inequality is approximately -11.04536. The inequality symbols suggest that the missing numbers should be less than this value on the left side and greater than this value on the right side. Given the context of the problem and based on what is shown in the image, a complete statement could be: Some number x < -√122 < Some number y where x is less than approximately -11.04536 and y is greater than approximately -11.04536. The actual values of x and y were not provided in the image.
Inequality Statement with Square Root of 68
The task here appears to be to fill in the blanks with numbers to make the inequality statement true, with the middle term being the square root of 68. To solve this, we first find the approximate value of the square root of 68. We know that: - √64 = 8 - √81 = 9 Since 68 is between 64 and 81, √68 will be between 8 and 9. Now that we know √68 is between 8 and 9, we can fill in the blanks with numbers to make the statement true. A logical approach would be to use the numbers 8 and 9 since the square root of 68 is between them. The complete statement should read: 8 < √68 < 9 This means that the square root of 68 is greater than 8 and less than 9, which is a true statement.
Solving Inequality with Square Root Approximation
The image shows an inequality with a square root of 139, and you need to determine what numbers could go into the blank boxes so that the inequality is true. Firstly, let's find out the approximate value of √139 since it's not a perfect square. To get an idea of where it lies, you can compare it to perfect squares nearby. For instance: - √121 = 11 (since 11^2 = 121) - √144 = 12 (since 12^2 = 144) Since 139 is between 121 and 144, √139 will be between 11 and 12. Calculating the exact decimal would give you a better approximation: √139 ≈ 11.789... This means that we need to find integers that are immediately less than and greater than 11.789. The integer immediately less than 11.789 is 11, and the integer immediately greater than 11.789 is 12. Therefore, to satisfy the inequality, the numbers on the blank boxes should be 11 and 12 in that order: 11 < √139 < 12
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