Question

question
express in simplest radical form.
$\frac{sqrt{2646}}{sqrt{9}}$

Explanation:

Step1: Simplify denominator

$\sqrt{9} = 3$

Step2: Simplify numerator via prime factorization

First factor 2646: $2646 = 2 \times 3^3 \times 7^2$
$\sqrt{2646} = \sqrt{2 \times 3^2 \times 3 \times 7^2} = 3 \times 7 \times \sqrt{2 \times 3} = 21\sqrt{6}$

Step3: Divide simplified numerator by denominator

$\frac{21\sqrt{6}}{3}$

Step4: Simplify the fraction

$21 \div 3 = 7$

Answer:

$7\sqrt{6}$