Question

question express in simplest radical form. sqrt{5}sqrt{15} answer attempt 1 out of 2

Explanation:

Step1: Recall radical multiplication rule

The rule for multiplying square roots is $\sqrt{a} \times \sqrt{b}=\sqrt{ab}$ (where $a\geq0$ and $b\geq0$). We have the expression $5\sqrt{15}$, but wait, maybe there was a typo? Wait, looking at the image, it's $\sqrt{5}\times\sqrt{15}$? Wait, no, the user's image shows "5√15" or maybe $\sqrt{5}\times\sqrt{15}$? Wait, no, the problem is to express $5\sqrt{15}$? Wait, no, maybe it's $\sqrt{5}\times\sqrt{15}$? Wait, no, let's check. Wait, the problem is to express in simplest radical form: $5\sqrt{15}$? Wait, no, maybe the original is $\sqrt{5}\times\sqrt{15}$? Wait, no, let's re - examine. Wait, the user's image has "√5√15" (maybe $\sqrt{5}\times\sqrt{15}$). Let's assume that the expression is $\sqrt{5}\times\sqrt{15}$.

Using the radical multiplication rule $\sqrt{a}\times\sqrt{b}=\sqrt{ab}$, so $\sqrt{5}\times\sqrt{15}=\sqrt{5\times15}$.

Step2: Simplify the radicand

Calculate $5\times15 = 75$. So we have $\sqrt{75}$. Now, factor 75 into its prime factors: $75=25\times3$. And we know that $\sqrt{25\times3}=\sqrt{25}\times\sqrt{3}$ (by the same radical multiplication rule, in reverse: $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ for $a = 25$, $b = 3$). Since $\sqrt{25}=5$, then $\sqrt{75}=5\sqrt{3}$. Wait, but if the original expression was $5\sqrt{15}$, then $5\sqrt{15}$ is already in simplest radical form because 15 factors into $3\times5$, and there are no perfect square factors other than 1. But if the original was $\sqrt{5}\times\sqrt{15}$, then we get $5\sqrt{3}$. Wait, maybe the user made a typo, but looking at the image, it's "5√15" or "√5√15". Wait, let's check the image again. The image shows "Question Express in simplest radical form. √5√15" (maybe). So let's proceed with $\sqrt{5}\times\sqrt{15}$.

First, apply $\sqrt{a}\times\sqrt{b}=\sqrt{ab}$: $\sqrt{5}\times\sqrt{15}=\sqrt{5\times15}=\sqrt{75}$.

Then, factor 75: $75 = 25\times3$.

Then, $\sqrt{75}=\sqrt{25\times3}=\sqrt{25}\times\sqrt{3}=5\sqrt{3}$.

Wait, but if the expression is $5\sqrt{15}$, then $5\sqrt{15}$ is already simplified because 15 has no perfect square factors other than 1. But given the way the image is presented (with two square roots), it's more likely that the expression is $\sqrt{5}\times\sqrt{15}$.

Answer:

If the expression is $\sqrt{5}\times\sqrt{15}$, the simplest radical form is $5\sqrt{3}$. If the expression is $5\sqrt{15}$, then it is already in simplest radical form as $5\sqrt{15}$. But based on the visual (with two square roots), the answer is $5\sqrt{3}$.