Question

express in simplest radical form.
\\(\dfrac{\sqrt{972}}{\sqrt{4}}\\)
answer
attempt 1 out of 2
input box
submit answer
radical symbol button

Explanation:

Step1: Simplify the denominator

The denominator is $\sqrt{4}$, and we know that $\sqrt{4} = 2$ since $2\times2 = 4$.

Step2: Simplify the numerator

We need to simplify $\sqrt{972}$. First, factor 972: $972=36\times27$. Then, using the property of square roots $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (where $a = 36$ and $b = 27$), we get $\sqrt{972}=\sqrt{36\times27}=\sqrt{36}\times\sqrt{27}$. Since $\sqrt{36} = 6$, this becomes $6\sqrt{27}$. Now, factor 27: $27 = 9\times3$, so $\sqrt{27}=\sqrt{9\times3}=\sqrt{9}\times\sqrt{3}=3\sqrt{3}$. Then $\sqrt{972}=6\times3\sqrt{3}=18\sqrt{3}$.

Step3: Divide the simplified numerator by the simplified denominator

We have $\frac{\sqrt{972}}{\sqrt{4}}=\frac{18\sqrt{3}}{2}$. Dividing 18 by 2 gives 9, so the result is $9\sqrt{3}$.

Answer:

$9\sqrt{3}$