Final answer:
The square roots of 16, 25, 9, 49, 36, 64, and 81 are 4, 5, 3, 7, 6, 8, and 9 respectively. These values are used to simplify the given expressions, resulting in 4, (5 + 3), (7 - 6), and (8 * 9), leading to final simplified results of 4, 8, 1, and 72.
Step-by-step explanation:
To simplify radical expressions, you need to find the square root of each number and perform the indicated operations. Let's walk through each step: a) \(\sqrt{16}\) The square root of 16 is 4, because \(4 \times 4 = 16\). Therefore, the simplified form of \(\sqrt{16}\) is 4. b) \(\sqrt{25} + \sqrt{9}\) First, find the square root of 25, which is 5, because \(5 \times 5 = 25\).
Next, find the square root of 9, which is 3, because \(3 \times 3 = 9\). Add these two square roots together to get \(5 + 3 = 8\). Hence, \(\sqrt{25} + \sqrt{9} = 8\). c) \(\sqrt{49} - \sqrt{36}\) Find the square root of 49, which is 7, since \(7 \times 7 = 49\). Then, find the square root of 36, which is 6, because \(6 \times 6 = 36\). Subtract \(6\) from \(7\) to get \(7 - 6 = 1\). Thus, \(\sqrt{49} - \sqrt{36} = 1\).
d) \(\sqrt{64} \cdot \sqrt{81}\) The square root of 64 is 8, as \(8 \times 8 = 64\). The square root of 81 is 9, because \(9 \times 9 = 81\). Multiply \(8\) by \(9\) to get \(8 \cdot 9 = 72\). Therefore, \(\sqrt{64} \cdot \sqrt{81} = 72\). In conclusion, the simplified radical expressions are: a) 4 b) 8 c) 1 d) 72