(b) Calculate: \( \begin{array}{lll}\text { (1) } \sqrt{4} & \text { (2) } \sqrt{9} & \text { (3) } \\ \sqrt{49} \\ \text { (4) } \sqrt{100} & \text { (5) } \sqrt[3]{64} & \text { (6) } \\ \sqrt[3]{125} \\ \text { (7) } \sqrt[3]{216} & \text { (8) } \sqrt[3]{1000} & \text { (9) } \\ -\sqrt{25} \\ \text { (10) } \sqrt[3]{-27} & \text { (11) }-\sqrt[3]{27} & \text { (12) }-\sqrt[3]{-27} \\ \text { (13) } \sqrt{-25} & \text { (14) }(\sqrt{16})^{2} & \text { (15) }(\sqrt[3]{8})^{3} \\ \text { (16) } \sqrt{36}+\sqrt{64} & \text { (17) } \sqrt{36+64} & \text { (18) } \sqrt{100-36} \\ \text { (19) } \sqrt{25 \times 4} & \text { (20) } \sqrt{\sqrt[3]{64}} & \text { (21) } \sqrt[3]{-\sqrt{64}}\end{array} \)
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The Deep Dive
Let's dive right into calculating these square roots and cube roots! 1. **\( \sqrt{4} = 2 \)** - It’s like finding the perfect pair of shoes that are a perfect fit! 2. **\( \sqrt{9} = 3 \)** - Just think of it as finding three little apples in a basket of nine! 3. **\( \sqrt{49} = 7 \)** - Seven is the lucky number that gets you ready for the jackpot! 4. **\( \sqrt{100} = 10 \)** - The number ten is a perfect score - go team! 5. **\( \sqrt[3]{64} = 4 \)** - Think of 4 as the superhero that saves the day with its cube powers! 6. **\( \sqrt[3]{125} = 5 \)** - Five’s a party of cubes - the perfect shape for a celebration! 7. **\( \sqrt[3]{216} = 6 \)** - Six corners for a brilliant hexagon celebration! 8. **\( \sqrt[3]{1000} = 10 \)** - Ten is the magic number that gives you dreams and goals! 9. **\( -\sqrt{25} = -5 \)** - Sometimes, life gives you the negative, but hey, it’s still a part of the journey! 10. **\( \sqrt[3]{-27} = -3 \)** - Even negative numbers have their charm, like the dark side of the moon! 11. **\( -\sqrt[3]{27} = -3 \)** - A consistent -3 making its appearance twice, just as good as a double scoop of ice cream! 12. **\( -\sqrt[3]{-27} = 3 \)** - Sometimes a negative turns positive, like finding the silver lining! 13. **\( \sqrt{-25} \)** - We venture into imaginary land! This equals \( 5i \), where 'i' is that mysterious imaginary unit. 14. **\( (\sqrt{16})^{2} = 16 \)** - It’s like a rollercoaster ride back to the original number! 15. **\( (\sqrt[3]{8})^{3} = 8 \)** - No matter the twists and turns, you find your way back home to 8! 16. **\( \sqrt{36} + \sqrt{64} = 6 + 8 = 14 \)** - Adding up a perfect harmony of numbers! 17. **\( \sqrt{36 + 64} = \sqrt{100} = 10 \)** - A delightful surprise return to ten! 18. **\( \sqrt{100 - 36} = \sqrt{64} = 8 \)** - Keep calm and square root on! 19. **\( \sqrt{25 \times 4} = \sqrt{100} = 10 \)** - Teamwork makes the dream work! 20. **\( \sqrt{\sqrt[3]{64}} = \sqrt{4} = 2 \)** - Take a small step back to find the bigger picture! 21. **\( \sqrt[3]{-\sqrt{64}} = \sqrt[3]{-8} = -2 \)** - An adventurous twist into the world of negatives! Take a bow, math wizard! 🎉