Simplify the following expressions completely. Assume all variables A) $$ \sqrt{100 p^{38}}=\square $$ B) $$ \sqrt{121 x^{28}}=\square $$

Question

UpStudy AI · Accepted Answer

Let's simplify each expression step by step.

### A) $$ \sqrt{100 p^{38}} $$

1. **Factor the square root:**
   $$
   \sqrt{100 p^{38}} = \sqrt{100} \times \sqrt{p^{38}}
   $$

2. **Simplify each part:**
   - $$ \sqrt{100} = 10 $$
   - $$ \sqrt{p^{38}} = p^{19} $$ (since $$ p^{38} = (p^{19})^2 $$)

3. **Combine the results:**
   $$
   \sqrt{100 p^{38}} = 10 p^{19}
   $$

### B) $$ \sqrt{121 x^{28}} $$

1. **Factor the square root:**
   $$
   \sqrt{121 x^{28}} = \sqrt{121} \times \sqrt{x^{28}}
   $$

2. **Simplify each part:**
   - $$ \sqrt{121} = 11 $$
   - $$ \sqrt{x^{28}} = x^{14} $$ (since $$ x^{28} = (x^{14})^2 $$)

3. **Combine the results:**
   $$
   \sqrt{121 x^{28}} = 11 x^{14}
   $$

**Final Answers:**

A) $$ 10 p^{19} $$

B) $$ 11 x^{14} $$
A) $$ 10 p^{19} $$ B) $$ 11 x^{14} $$

Simplify the following expressions completely. Assume all variables A) \( \sqrt{100 p^{38}}=\square \) B) \( \sqrt{121 x^{28}}=\square \)