Make me SIMPLE DIRECTION: Write each radical in simplest form. $$ \begin{array}{lll} ext { 1. } \sqrt{\frac{9}{16}} & ext { 4. } \frac{2}{\sqrt{2}} \ ext { 2. } \frac{\sqrt{25}}{\sqrt{100}} & ext { 5. } & -\frac{1}{3 \sqrt{2}} \ ext { 3. } & -\sqrt{\frac{4}{5}}\end{array} $$

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Make me SIMPLE DIRECTION: Write each radical in simplest form. $$ \begin{array}{lll}	ext { 1. } \sqrt{\frac{9}{16}} & 	ext { 4. } \frac{2}{\sqrt{2}} \ 	ext { 2. } \frac{\sqrt{25}}{\sqrt{100}} & 	ext { 5. } & -\frac{1}{3 \sqrt{2}} \ 	ext { 3. } & -\sqrt{\frac{4}{5}}\end{array} $$

UpStudy AI · Accepted Answer

Sure! Let's simplify each radical step by step.

### 1. $$ \sqrt{\frac{9}{16}} $$

$$
\sqrt{\frac{9}{16}} = \frac{\sqrt{9}}{\sqrt{16}} = \frac{3}{4}
$$

**Simplified Form:** $$ \frac{3}{4} $$

---

### 2. $$ \frac{\sqrt{25}}{\sqrt{100}} $$

$$
\frac{\sqrt{25}}{\sqrt{100}} = \frac{5}{10} = \frac{1}{2}
$$

**Simplified Form:** $$ \frac{1}{2} $$

---

### 3. $$ -\sqrt{\frac{4}{5}} $$

First, simplify the square root:

$$
-\sqrt{\frac{4}{5}} = -\frac{\sqrt{4}}{\sqrt{5}} = -\frac{2}{\sqrt{5}}
$$

To rationalize the denominator:

$$
-\frac{2}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = -\frac{2\sqrt{5}}{5}
$$

**Simplified Form:** $$ -\frac{2\sqrt{5}}{5} $$

---

### 4. $$ \frac{2}{\sqrt{2}} $$

Rationalize the denominator:

$$
\frac{2}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{2\sqrt{2}}{2} = \sqrt{2}
$$

**Simplified Form:** $$ \sqrt{2} $$

---

### 5. $$ -\frac{1}{3\sqrt{2}} $$

Rationalize the denominator:

$$
-\frac{1}{3\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = -\frac{\sqrt{2}}{3 \times 2} = -\frac{\sqrt{2}}{6}
$$

**Simplified Form:** $$ -\frac{\sqrt{2}}{6} $$

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### Summary of Simplified Radicals

1. $$ \frac{3}{4} $$
2. $$ \frac{1}{2} $$
3. $$ -\frac{2\sqrt{5}}{5} $$
4. $$ \sqrt{2} $$
5. $$ -\frac{\sqrt{2}}{6} $$
1. $$ \frac{3}{4} $$ 2. $$ \frac{1}{2} $$ 3. $$ -\frac{2\sqrt{5}}{5} $$ 4. $$ \sqrt{2} $$ 5. $$ -\frac{\sqrt{2}}{6} $$

Make me SIMPLE DIRECTION: Write each radical in simplest form. \( \begin{array}{lll}\text { 1. } \sqrt{\frac{9}{16}} & \text { 4. } \frac{2}{\sqrt{2}} \\ \text { 2. } \frac{\sqrt{25}}{\sqrt{100}} & \text { 5. } & -\frac{1}{3 \sqrt{2}} \\ \text { 3. } & -\sqrt{\frac{4}{5}}\end{array} \)

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