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Enter the values for the variables that give the correct simplified expressions, [tex]x \geq 0[/tex].

[tex]\[
\begin{array}{l}
\sqrt{50 x^2} = \sqrt{25 \cdot 2 \cdot x^2} = 5 x \sqrt{2} \\
b = 2 \\
\sqrt{32 x} = \sqrt{16 \cdot 2 \cdot x} = 4 \sqrt{2 x} \\
c = 4 \\
\sqrt{18 n} = \sqrt{9 \cdot 2 \cdot n} = 3 \sqrt{2 n} \\
e = 3 \\
\sqrt{72 x^2} = \sqrt{36 \cdot 2 \cdot x^2} = 6 x \sqrt{2} \\
g = 6
\end{array}
\][/tex]

Sagot :

GinnyAnswer
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]
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