To find the values of [tex]\( b, c, e, \)[/tex] and [tex]\( g \)[/tex], we need to simplify the given square root expressions.
1. For the expression [tex]\(\sqrt{50 x^2}\)[/tex]:
[tex]\[
\sqrt{50 x^2} = \sqrt{25 \cdot 2 \cdot x^2}
\][/tex]
We can simplify this as:
[tex]\[
\sqrt{50 x^2} = \sqrt{25} \cdot \sqrt{2} \cdot \sqrt{x^2} = 5 x \sqrt{2}
\][/tex]
Therefore,
[tex]\[
5 x \sqrt{b} = 5 x \sqrt{2}
\][/tex]
This means:
[tex]\[
b = 2
\][/tex]
2. For the expression [tex]\(\sqrt{32 x}\)[/tex]:
[tex]\[
\sqrt{32 x} = \sqrt{16 \cdot 2 \cdot x}
\][/tex]
We can simplify this as:
[tex]\[
\sqrt{32 x} = \sqrt{16} \cdot \sqrt{2} \cdot \sqrt{x} = 4 \sqrt{2} \sqrt{x} = 4 \sqrt{2 x}
\][/tex]
Therefore,
[tex]\[
c \sqrt{2 x} = 4 \sqrt{2 x}
\][/tex]
This means:
[tex]\[
c = 4
\][/tex]
3. For the expression [tex]\(\sqrt{18 n}\)[/tex]:
[tex]\[
\sqrt{18 n} = \sqrt{9 \cdot 2 \cdot n}
\][/tex]
We can simplify this as:
[tex]\[
\sqrt{18 n} = \sqrt{9} \cdot \sqrt{2} \cdot \sqrt{n} = 3 \sqrt{2} \sqrt{n} = 3 \sqrt{2 n}
\][/tex]
Therefore,
[tex]\[
e \sqrt{2 n} = 3 \sqrt{2 n}
\][/tex]
This means:
[tex]\[
e = 3
\][/tex]
4. For the expression [tex]\(\sqrt{72 x^2}\)[/tex]:
[tex]\[
\sqrt{72 x^2} = \sqrt{36 \cdot 2 \cdot x^2}
\][/tex]
We can simplify this as:
[tex]\[
\sqrt{72 x^2} = \sqrt{36} \cdot \sqrt{2} \cdot \sqrt{x^2} = 6 x \sqrt{2}
\][/tex]
Therefore,
[tex]\[
g x \sqrt{2} = 6 x \sqrt{2}
\][/tex]
This means:
[tex]\[
g = 6
\][/tex]
So the values are:
[tex]\[
b = 2, \quad c = 4, \quad e = 3, \quad g = 6
\][/tex]
