Simplify. sqrt 105/4 ______

Apply Quotient Rule: Apply the quotient rule of radicals to sqrt(105/4). sqrt(105/4) = sqrt(105) / sqrt(4)Evaluate sqrt(105): Evaluate sqrt(105). Find the prime factorization of 105 and try to make identical pairs of factors. sqrt(105) = sqrt(3 * 5 * 7) Since there are no pairs of identical factors, we cannot simplify it further.Find Prime Factorization: Now, let's evaluate sqrt(4). sqrt(4) = sqrt(2 * 2) = 2Evaluate sqrt(4): Combine the results from the previous steps. sqrt(105/4) = sqrt(105) / sqrt(4) = (sqrt(105)) / 2 = (sqrt(3 * 5 * 7)) / 2 = (sqrt(3) * sqrt(5) * sqrt(7)) / 2 Since none of the square roots can be simplified further, this is the final simplified form.

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Simplify. $\newline$ $\sqrt{\frac{105}{4}}$

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Algebra 2

Simplify radical expressions involving fractions

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Q. Simplify.

\newline

\sqrt{\frac{105}{4}}

Apply Quotient Rule: Apply the quotient rule of radicals to $\sqrt{\frac{105}{4}}$ . $\sqrt{\frac{105}{4}} = \frac{\sqrt{105}}{\sqrt{4}}$
Evaluate $\sqrt{105}$ : Evaluate $\sqrt{105}$ . Find the prime factorization of $105$ and try to make identical pairs of factors. $\sqrt{105} = \sqrt{3 \times 5 \times 7}$ Since there are no pairs of identical factors, we cannot simplify it further.
Find Prime Factorization: Now, let's evaluate $\sqrt{4}$ . $\newline$ $\sqrt{4} = \sqrt{2 \times 2}$ $\newline$ = $2$
Evaluate $\sqrt{4}$ : Combine the results from the previous steps. $\newline$ \sqrt{\frac{105}{4}} = \frac{\sqrt{105}}{\sqrt{4}}$\newline= \frac{\sqrt{105}}{2} $\newline$ = \frac{\sqrt{3 \times 5 \times 7}}{2} $\newline$ = \frac{\sqrt{3} \times \sqrt{5} \times \sqrt{7}}{2}$ $\newline$ Since none of the square roots can be simplified further, this is the final simplified form.