1. Rewrite the irrational square root √48 as the product of an integer and another irrational square root.(1 point)

2. What is the irrational square root √28 simplified?

3. Rewrite the irrational cube root ^3√48 as a product of an integer and another irrational cube root.

4. What is the irrational cube root ^3√−24 rewritten as a product of an integer and another irrational cube root?

5. What is the irrational cube root ^3√40 rewritten as a product of an integer and another irrational cube root?

3 answers

  1. To rewrite the irrational square root \( \sqrt{48} \) as a product of an integer and another irrational square root, we can factor 48: \[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}. \]

  2. To simplify \( \sqrt{28} \): \[ \sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7} = 2\sqrt{7}. \]

  3. To rewrite the irrational cube root \( \sqrt[3]{48} \) as a product of an integer and another irrational cube root, we factor 48: \[ \sqrt[3]{48} = \sqrt[3]{8 \times 6} = \sqrt[3]{8} \times \sqrt[3]{6} = 2\sqrt[3]{6}. \]

  4. To rewrite the irrational cube root \( \sqrt[3]{-24} \): \[ \sqrt[3]{-24} = \sqrt[3]{-8 \times 3} = \sqrt[3]{-8} \times \sqrt[3]{3} = -2\sqrt[3]{3}. \]

  5. To rewrite the irrational cube root \( \sqrt[3]{40} \): \[ \sqrt[3]{40} = \sqrt[3]{8 \times 5} = \sqrt[3]{8} \times \sqrt[3]{5} = 2\sqrt[3]{5}. \]

as a list

Sure! Here’s the information presented as a list:

  1. \( \sqrt{48} = 4\sqrt{3} \)

  2. \( \sqrt{28} = 2\sqrt{7} \)

  3. \( \sqrt[3]{48} = 2\sqrt[3]{6} \)

  4. \( \sqrt[3]{-24} = -2\sqrt[3]{3} \)

  5. \( \sqrt[3]{40} = 2\sqrt[3]{5} \)