https://file.aiquickdraw.com/mathbot/file/1726620318333l5uqnjd1.jpg

Let's solve the square root operations from the image one by one.

### 1. \( 5\sqrt{2} + \sqrt{2} - 3\sqrt{2} \)

Combine like terms:

\[
(5 + 1 - 3)\sqrt{2} = 3\sqrt{2}
\]

So, the result is \( \boxed{3\sqrt{2}} \).

---

### 2. \( 3\sqrt{24} - \sqrt{150} + 2\sqrt{54} \)

First, simplify the square roots:
- \( \sqrt{24} = \sqrt{4 \times 6} = 2\sqrt{6} \)
- \( \sqrt{150} = \sqrt{25 \times 6} = 5\sqrt{6} \)
- \( \sqrt{54} = \sqrt{9 \times 6} = 3\sqrt{6} \)

Now substitute into the expression:

\[
3\sqrt{24} - \sqrt{150} + 2\sqrt{54} = 3(2\sqrt{6}) - 5\sqrt{6} + 2(3\sqrt{6}) 
\]
\[
= 6\sqrt{6} - 5\sqrt{6} + 6\sqrt{6} 
\]
\[
= (6 - 5 + 6)\sqrt{6} = 7\sqrt{6}
\]

So, the result is \( \boxed{7\sqrt{6}} \).

---

### 3. \( 2\sqrt{72} - 5\sqrt{32} + 3\sqrt{162} \)

First, simplify the square roots:
- \( \sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2} \)
- \( \sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2} \)
- \( \sqrt{162} = \sqrt{81 \times 2} = 9\sqrt{2} \)

Now substitute into the expression:

\[
2\sqrt{72} - 5\sqrt{32} + 3\sqrt{162} = 2(6\sqrt{2}) - 5(4\sqrt{2}) + 3(9\sqrt{2})
\]
\[
= 12\sqrt{2} - 20\sqrt{2} + 27\sqrt{2}
\]
\[
= (12 - 20 + 27)\sqrt{2} = 19\sqrt{2}
\]

So, the result is \( \boxed{19\sqrt{2}} \).

---

### 4. \( (4\sqrt{2})(\sqrt{2} + \sqrt{3}) \)

Distribute \( 4\sqrt{2} \):

\[
4\sqrt{2} \times \sqrt{2} + 4\sqrt{2} \times \sqrt{3} 
\]
\[
= 4(2) + 4\sqrt{6} 
\]
\[
= 8 + 4\sqrt{6}
\]

So, the result is \( \boxed{8 + 4\sqrt{6}} \).

---

### 5. \( (3 - \sqrt{5})(3 + \sqrt{5}) \)

This is a difference of squares:

\[
(3 - \sqrt{5})(3 + \sqrt{5}) = 3^2 - (\sqrt{5})^2
\]
\[
= 9 - 5 = 4
\]

So, the result is \( \boxed{4} \).

---

Let me know if you need more details or have any questions! Here are some additional questions you can explore:

1. How do you simplify radical expressions like \( \sqrt{24} \)?
2. Why does \( (a - b)(a + b) \) give a difference of squares?
3. Can you expand \( (2 + \sqrt{3})(2 - \sqrt{3}) \) using the same difference of squares formula?
4. How do you combine like terms with radicals, such as \( 5\sqrt{6} + 3\sqrt{6} \)?
5. How can you simplify the expression \( 2\sqrt{18} + 3\sqrt{8} \)?

### Tip:
When simplifying square roots, try factoring numbers into perfect squares for easier simplification.

Tentukan hasil dari operasi bentuk akar berikut: 1. 5√2 + √2 - 3√2, 2. 3√24 - √150 + 2√54, 3. 2√72 - 5√32 + 3√162, 4. (4√2)(√2 + √3), 5. (3 - √5)(3 + √5)

Learn how to simplify radical expressions involving square roots and the difference of squares formula. This problem covers topics such as combining like terms with square roots and applying the difference of squares theorem. Suitable for high school students in Grades 9-12.

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