Answer :
To simplify the expression
[tex]$$
\sqrt{\frac{45}{12}},
$$[/tex]
follow these steps:
1. Simplify the Fraction:
Divide both the numerator and the denominator by their greatest common divisor, which is [tex]$3$[/tex]. This yields
[tex]$$
\frac{45}{12} = \frac{45 \div 3}{12 \div 3} = \frac{15}{4}.
$$[/tex]
2. Apply the Square Root:
Rewrite the square root of the fraction as the fraction of square roots:
[tex]$$
\sqrt{\frac{15}{4}} = \frac{\sqrt{15}}{\sqrt{4}}.
$$[/tex]
3. Simplify the Denominator:
Since [tex]$\sqrt{4} = 2$[/tex], the expression becomes
[tex]$$
\frac{\sqrt{15}}{2}.
$$[/tex]
Thus, the simplified form of the original expression is
[tex]$$
\boxed{\frac{\sqrt{15}}{2}}.
$$[/tex]
[tex]$$
\sqrt{\frac{45}{12}},
$$[/tex]
follow these steps:
1. Simplify the Fraction:
Divide both the numerator and the denominator by their greatest common divisor, which is [tex]$3$[/tex]. This yields
[tex]$$
\frac{45}{12} = \frac{45 \div 3}{12 \div 3} = \frac{15}{4}.
$$[/tex]
2. Apply the Square Root:
Rewrite the square root of the fraction as the fraction of square roots:
[tex]$$
\sqrt{\frac{15}{4}} = \frac{\sqrt{15}}{\sqrt{4}}.
$$[/tex]
3. Simplify the Denominator:
Since [tex]$\sqrt{4} = 2$[/tex], the expression becomes
[tex]$$
\frac{\sqrt{15}}{2}.
$$[/tex]
Thus, the simplified form of the original expression is
[tex]$$
\boxed{\frac{\sqrt{15}}{2}}.
$$[/tex]
