Example Question - square root range
Here are examples of questions we've helped users solve.
Understanding Number Range Around Square Roots
The question in the image seems to be asking to fill in the blanks with numbers that are less than and greater than the square root of 34, respectively. Let's find two perfect squares that are close to 34 to help us find the square root range of 34: Taking perfect squares near 34: - \(5^2 = 25\) - \(6^2 = 36\) Since 25 is less than 34, and 36 is greater than 34, the square root of 34 will be between 5 and 6. Therefore, a number less than square root of 34 would be 5 (or any number between 5 and \(\sqrt{34}\) that's not an integer), and a number greater than square root of 34 would be 6 (or any number between \(\sqrt{34}\) and 6 that's not an integer). So, the blanks should be filled with: 5 < \(\sqrt{34}\) < 6
Determining Perfect Squares for Square Root Range
The question in the image asks to find two perfect squares between which the square root of 34 falls. Since \(\sqrt{34}\) is not a whole number, we know it lies between two consecutive integer square roots. To determine these, we find the perfect squares nearest to 34 on either side. The perfect square less than 34 is \(5^2 = 25\), and the perfect square greater than 34 is \(6^2 = 36\). Hence, \(\sqrt{25}\) is 5, and \(\sqrt{36}\) is 6. So the square root of 34 falls between the square roots of 25 and 36. Therefore, the inequalities are: \[ 5 < \sqrt{34} < 6 \] In the provided boxes, the numbers 5 and 6 would fit appropriately to show the inequality. \[ 5 < \sqrt{34} < 6 \]
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