Use the product and quotient rules for radicals to rewrite eac...

Question

Use the product and quotient rules for radicals to rewrite each expression. See Example 4. √3 • √27

Accepted Answer

Hey, everyone here we are asked to rewrite the given radical expression. Using the product rule. Here we are given the square root of seven multiplied by the square root of 343. Here we have four answer choice options, answer choice A seven multiplied by the square root of seven. Answer B 49 answer C 343 and answer D 49 multiplied by the square root of seven. So to begin this problem, we need to recall the product rule of radicals which states that the square root of A multiplied by the square root of B is equivalent to the square root of a multiplied by B. So now rewriting our given expression following the product rule, we can first notice that the value of A is going to be seven. And that means the value for B is 343. So now rewriting our expression, we have the square root of seven multiplied by 343. So now finding the product of these two values, we can rewrite our expression as the square root of 2401. So now the next step is to start simplifying our expression. So we just want to rewrite the value underneath the square root as its square. So we rewrite 2401 as 49 squared. So now our expression is the square root of squared. Now continuing to simplify, we are taking the square root of a square. So we are just left with the base. So our expression simplifies to 49. And with this value, we are left with answer choice B where again, our simplified expression just leaves us with 49. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Use the product and quotient rules for radicals to rewrite each expression. See Example 4. √3 • √27

Key Concepts

Product Rule for Radicals

Simplifying Radicals

Quotient Rule for Radicals

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