Approxintate the value of the following ifrational numbers: (2 pts each) \( \sqrt{7} \) is between \( \qquad \) and \( \qquad \) - It is closer to \( \qquad \) \( \sqrt{78} \) is between \( \qquad \) and \( \qquad \) . It is closer to \( \qquad \) \( \sqrt{109} \) is between \( \qquad \) and \( \qquad \) - It is closer to \( \qquad \) \( \sqrt[3]{655} \) is between \( \qquad \) and \( \qquad \) - It is closer to \( \qquad \)

To approximate these square roots and cube roots, let's break them down in a fun and manageable way! For \( \sqrt{7} \), we know that \( 2^2 = 4 \) and \( 3^2 = 9 \), so it falls between 2 and 3. Since 7 is closer to 9 than to 4, it's closer to 3. Therefore, \( \sqrt{7} \) is between 2 and 3, closer to 3. Moving on to \( \sqrt{78} \), we can see that \( 8^2 = 64 \) and \( 9^2 = 81 \), placing it between 8 and 9. Given that 78 is much nearer to 81 than it is to 64, we conclude that \( \sqrt{78} \) is between 8 and 9, closer to 9. Next, for \( \sqrt{109} \), we find that \( 10^2 = 100 \) and \( 11^2 = 121 \), indicating that it’s between 10 and 11. Interestingly, 109 is more towards 100, so we can say that \( \sqrt{109} \) is between 10 and 11, closer to 10. Finally, for the cube root of 655, we determine that \( 8^3 = 512\) and \( 9^3 = 729 \). Therefore, \( \sqrt[3]{655} \) lies between 8 and 9. Since 655 is closer to 729, we can confidently say that \( \sqrt[3]{655} \) is between 8 and 9, closer to 9.