$$ \begin{array}{ll}\sqrt[2]{8}=\square & ext { b. } \sqrt[3]{64}=\square \ \sqrt{9}+\sqrt{16}= & ext { b. } \sqrt{100}+\sqrt{81}= \ \sqrt[3]{216}+\sqrt[3]{27}= & ext { b. } \sqrt[3]{27}-\sqrt[3]{8}=\end{array} $$

Question

$$ \begin{array}{ll}\sqrt[2]{8}=\square & 	ext { b. } \sqrt[3]{64}=\square \ \sqrt{9}+\sqrt{16}= & 	ext { b. } \sqrt{100}+\sqrt{81}= \ \sqrt[3]{216}+\sqrt[3]{27}= & 	ext { b. } \sqrt[3]{27}-\sqrt[3]{8}=\end{array} $$

UpStudy AI · Accepted Answer

Sure, let's solve each of the given expressions by filling in the blanks.

### 1. Square Roots
- **a.** $$ \sqrt{8} = 2\sqrt{2} $$
  
  *Explanation:* $$ \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2} $$

- **b.** $$ \sqrt[3]{64} = 4 $$
  
  *Explanation:* $$ 4^3 = 64 $$, so the cube root of 64 is 4.

### 2. Addition of Square Roots
- **a.** $$ \sqrt{9} + \sqrt{16} = 3 + 4 = 7 $$
  
  *Explanation:* $$ \sqrt{9} = 3 $$ and $$ \sqrt{16} = 4 $$. Adding them gives $$ 3 + 4 = 7 $$.

- **b.** $$ \sqrt{100} + \sqrt{81} = 10 + 9 = 19 $$
  
  *Explanation:* $$ \sqrt{100} = 10 $$ and $$ \sqrt{81} = 9 $$. Adding them gives $$ 10 + 9 = 19 $$.

### 3. Operations with Cube Roots
- **a.** $$ \sqrt[3]{216} + \sqrt[3]{27} = 6 + 3 = 9 $$
  
  *Explanation:* $$ \sqrt[3]{216} = 6 $$ (since $$ 6^3 = 216 $$) and $$ \sqrt[3]{27} = 3 $$ (since $$ 3^3 = 27 $$). Adding them gives $$ 6 + 3 = 9 $$.

- **b.** $$ \sqrt[3]{27} - \sqrt[3]{8} = 3 - 2 = 1 $$
  
  *Explanation:* $$ \sqrt[3]{27} = 3 $$ and $$ \sqrt[3]{8} = 2 $$. Subtracting them gives $$ 3 - 2 = 1 $$.

### Summary of Answers
$$
\begin{array}{ll}
\sqrt{8}=2\sqrt{2} & \text{b. } \sqrt[3]{64}=4 \
\sqrt{9}+\sqrt{16}=7 & \text{b. } \sqrt{100}+\sqrt{81}=19 \
\sqrt[3]{216}+\sqrt[3]{27}=9 & \text{b. } \sqrt[3]{27}-\sqrt[3]{8}=1 \
\end{array}
$$

Feel free to ask if you have any more questions!
$$ \begin{array}{ll} \sqrt{8} = 2\sqrt{2} & \sqrt[3]{64} = 4 \ \sqrt{9} + \sqrt{16} = 7 & \sqrt{100} + \sqrt{81} = 19 \ \sqrt[3]{216} + \sqrt[3]{27} = 9 & \sqrt[3]{27} - \sqrt[3]{8} = 1 \ \end{array} $$

Upstudy AI Solution

Answer

Solution

1. Square Roots

2. Addition of Square Roots

3. Operations with Cube Roots

Summary of Answers

Bonus Knowledge

Related Questions

Latest Pre Algebra Questions