Question

find the cubic root of 189.
27^3√7
9^3√21
3√7
3^3√7

Answer 1

To find the cubic root of 189, we can simplify it as follows:

First, the prime factorization of 189:
189 = 3 × 63
63 = 3 × 21
21 = 3 × 7

So, we have:
189 = \(3^3 \times 7\)

Now we can find the cubic root:
\[
\sqrt[3]{189} = \sqrt[3]{3^3 \times 7} = \sqrt[3]{3^3} \times \sqrt[3]{7} = 3 \times \sqrt[3]{7}
\]

Thus, \(\sqrt[3]{189} = 3 \sqrt[3]{7}\).

Now let's check the given options to see which one matches:

1. \(27^\frac{1}{3}\sqrt{7} = 3\sqrt[3]{7}\)
2. \(9^\frac{1}{3}\sqrt{21}\)
3. \(3\sqrt[3]{7}\)
4. \(3^\frac{1}{3}\sqrt{7}\)

The correct answer is \(3\sqrt[3]{7}\).