Let's simplify each of the given expressions step by step to find the values for the variables [tex]\( b \)[/tex], [tex]\( c \)[/tex], [tex]\( e \)[/tex], and [tex]\( g \)[/tex]:
1. [tex]\(\sqrt{50x^2}\)[/tex]:
[tex]\[
\sqrt{50x^2} = \sqrt{25 \cdot 2 \cdot x^2}
\][/tex]
We know that [tex]\(\sqrt{25} = 5\)[/tex] and [tex]\(\sqrt{x^2} = x\)[/tex], so we can simplify this expression as:
[tex]\[
\sqrt{25 \cdot 2 \cdot x^2} = 5x\sqrt{2}
\][/tex]
Thus, the value of [tex]\( b \)[/tex] is:
[tex]\[
b = 2
\][/tex]
2. [tex]\(\sqrt{32x}\)[/tex]:
[tex]\[
\sqrt{32x} = \sqrt{16 \cdot 2 \cdot x}
\][/tex]
We know that [tex]\(\sqrt{16} = 4\)[/tex], so we can simplify this expression as:
[tex]\[
\sqrt{16 \cdot 2 \cdot x} = 4\sqrt{2x}
\][/tex]
Thus, the value of [tex]\( c \)[/tex] is:
[tex]\[
c = 4
\][/tex]
3. [tex]\(\sqrt{18n}\)[/tex]:
[tex]\[
\sqrt{18n} = \sqrt{9 \cdot 2 \cdot n}
\][/tex]
We know that [tex]\(\sqrt{9} = 3\)[/tex], so we can simplify this expression as:
[tex]\[
\sqrt{9 \cdot 2 \cdot n} = 3\sqrt{2n}
\][/tex]
Thus, the value of [tex]\( e \)[/tex] is:
[tex]\[
e = 3
\][/tex]
4. [tex]\(\sqrt{72x^2}\)[/tex]:
[tex]\[
\sqrt{72x^2} = \sqrt{36 \cdot 2 \cdot x^2}
\][/tex]
We know that [tex]\(\sqrt{36} = 6\)[/tex] and [tex]\(\sqrt{x^2} = x\)[/tex], so we can simplify this expression as:
[tex]\[
\sqrt{36 \cdot 2 \cdot x^2} = 6x\sqrt{2}
\][/tex]
Thus, the value of [tex]\( g \)[/tex] is:
[tex]\[
g = 6
\][/tex]
In summary, the values are:
[tex]\[
b = 2 \\
c = 4 \\
e = 3 \\
g = 6
\][/tex]
