Use the product and quotient rules for radicals to rewrite each e...

Question

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

30√10
 5√2

Accepted Answer

Hey, everyone here we are asked to rewrite the given radical expression using the quotient rule. Here we are given 84 multiplied by the square root of 30 divided by 12, multiplied by the square root of five. Here we have four answer choice options, answer choice A seven multiplied by the square root of five. Answer B seven multiplied by the square root of six. Answer C six multiplied by the square root of seven and answer D 42. So before we can begin applying the quotient rule for the given expression, we first want to simplify it by noticing we have 84 in the numerator and 12 in the denominator and divided by 12 gives us seven. So we can simplify this given expression as seven multiplied by the square root of 30 divided by the square root of five. And with this simplified expression, we now want to recall the quotient rule of radicals which states that the square root of a divided by the square root of B is equivalent to the square root of A divided by B. So now using this quotient rule, we want to rewrite our simplified expression. So we have seven multiplied by the square root of 30 divided by five. And now we just want to simplify the value underneath the square root. So 30 divided by five gives us six. And so our expression simplifies 27 multiplied by the square root of six. And now there are no further simplifications that we can make to this expression. So we are left with answer choice B where again, our rewritten expression is seven multiplied by the square root of six. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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Use the product and quotient rules for radicals to rewrite each expression. See Example 4. 30√10 5√2