$$ \begin{array}{ll} ext { Simplify Radicals } \ \sqrt{125 v^{4}}= & \sqrt{6300}= \ \sqrt{180}= \ \sqrt[3]{8 y^{3}}= & \sqrt[4]{162 x^{5}}= \ 1\end{array} $$

Question

$$ \begin{array}{ll}	ext { Simplify Radicals } \ \sqrt{125 v^{4}}= & \sqrt{6300}= \ \sqrt{180}= \ \sqrt[3]{8 y^{3}}= & \sqrt[4]{162 x^{5}}= \ 1\end{array} $$

UpStudy AI · Accepted Answer

Sure, let's simplify each of the given radical expressions step by step.

### 1. Simplify $$ \sqrt{125v^{4}} $$

**Step-by-Step:**
$$
\sqrt{125v^{4}} = \sqrt{25 \times 5 \times v^{4}} = \sqrt{25} \times \sqrt{5} \times \sqrt{v^{4}} = 5 \times \sqrt{5} \times v^{2}
$$

**Simplified Form:**
$$
\sqrt{125v^{4}} = 5v^{2}\sqrt{5}
$$

---

### 2. Simplify $$ \sqrt{6300} $$

**Step-by-Step:**
$$
\sqrt{6300} = \sqrt{100 \times 63} = \sqrt{100} \times \sqrt{63} = 10 \times \sqrt{63}
$$
$$
\sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7} = 3\sqrt{7}
$$
$$
10 \times 3\sqrt{7} = 30\sqrt{7}
$$

**Simplified Form:**
$$
\sqrt{6300} = 30\sqrt{7}
$$

---

### 3. Simplify $$ \sqrt{180} $$

**Step-by-Step:**
$$
\sqrt{180} = \sqrt{36 \times 5} = \sqrt{36} \times \sqrt{5} = 6\sqrt{5}
$$

**Simplified Form:**
$$
\sqrt{180} = 6\sqrt{5}
$$

---

### 4. Simplify $$ \sqrt[3]{8y^{3}} $$

**Step-by-Step:**
$$
\sqrt[3]{8y^{3}} = \sqrt[3]{8} \times \sqrt[3]{y^{3}} = 2 \times y = 2y
$$

**Simplified Form:**
$$
\sqrt[3]{8y^{3}} = 2y
$$

---

### 5. Simplify $$ \sqrt[4]{162x^{5}} $$

**Step-by-Step:**
$$
\sqrt[4]{162x^{5}} = \sqrt[4]{81 \times 2 \times x^{4} \times x} = \sqrt[4]{81x^{4}} \times \sqrt[4]{2x}
$$
$$
\sqrt[4]{81x^{4}} = \sqrt[4]{81} \times \sqrt[4]{x^{4}} = 3 \times x = 3x
$$
$$
3x \times \sqrt[4]{2x} = 3x \sqrt[4]{2x}
$$

**Simplified Form:**
$$
\sqrt[4]{162x^{5}} = 3x\sqrt[4]{2x}
$$

---

### Summary of Simplified Radicals

$$
\begin{aligned}
\sqrt{125v^{4}} &= 5v^{2}\sqrt{5} \
\sqrt{6300} &= 30\sqrt{7} \
\sqrt{180} &= 6\sqrt{5} \
\sqrt[3]{8y^{3}} &= 2y \
\sqrt[4]{162x^{5}} &= 3x\sqrt[4]{2x}
\end{aligned}
$$

If you have any more radicals you'd like to simplify or need further explanations, feel free to ask!
$$ \begin{aligned} \sqrt{125v^{4}} &= 5v^{2}\sqrt{5} \ \sqrt{6300} &= 30\sqrt{7} \ \sqrt{180} &= 6\sqrt{5} \ \sqrt[3]{8y^{3}} &= 2y \ \sqrt[4]{162x^{5}} &= 3x\sqrt[4]{2x} \end{aligned} $$

Solución de inteligencia artificial de Upstudy

Responder

Solución

1. Simplify

2. Simplify

3. Simplify

4. Simplify

5. Simplify

Summary of Simplified Radicals

Mind Expander

preguntas relacionadas

Latest Pre Algebra Questions