Question

Find the square root of 169: 169−−−√
.(1 point)
Responses

13,−13
13 comma negative 13

84.5
84.5

13
13

−13

Answer 1

Find the cube root of −729
: −729−−−−√3
(1 point)
Responses

9
9

−9
negative 9

243
243

9, −9

Answer 2

Find the cube root of −8

Answer 3

Rewrite the irrational cube root 189−−−√3
as the product of an integer and another irrational cube root. Show your work.

Answer 4

The square root of 169 is \( 13 \) and also \( -13 \) since both \( 13^2 \) and \( (-13)^2 \) equal 169. Therefore, the correct answer is:

**13,−13** (13 comma negative 13)

Answer 5

The cube root of \(-729\) is \(-9\), since \((-9) \times (-9) \times (-9) = -729\). Therefore, the correct answer is:

**−9** (negative 9)

Answer 6

The cube root of \(-8\) is \(-2\), because \((-2) \times (-2) \times (-2) = -8\).

Answer 7

To rewrite \( \sqrt[3]{189} \) as the product of an integer and another irrational cube root, let's break down 189 into its prime factors.

First, we find the prime factorization of \( 189 \):

1. Divide \( 189 \) by \( 3 \):
\[
189 \div 3 = 63
\]
2. Divide \( 63 \) by \( 3 \):
\[
63 \div 3 = 21
\]
3. Divide \( 21 \) by \( 3 \):
\[
21 \div 3 = 7
\]
4. Knowing \( 7 \) is prime, we stop here.

Thus, the prime factorization of \( 189 \) is:
\[
189 = 3^3 \times 7
\]

Now we can rewrite \( \sqrt[3]{189} \):

\[
\sqrt[3]{189} = \sqrt[3]{3^3 \times 7}
\]

Using the property of cube roots, this can be separated into:

\[
\sqrt[3]{189} = \sqrt[3]{3^3} \times \sqrt[3]{7}
\]

Since \( \sqrt[3]{3^3} = 3 \), we have:

\[
\sqrt[3]{189} = 3 \times \sqrt[3]{7}
\]

Thus, \( \sqrt[3]{189} \) can be rewritten as the product of an integer and another irrational cube root:

\[
\sqrt[3]{189} = 3 \sqrt[3]{7}
\]