Question - Determining Perfect Squares for Square Root Range
Solution:
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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