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. √4⁄50

Accepted Answer

Hey, everyone. Here we are asked to rewrite the given radical expression using the quotient rule. Here we are given the square root of divided by 1859. Here we have four answer choice options, answer choice A, the square root of 13 divided by 11, answer B one divided by 13, answer C the square root of 11 divided by 13 and answer D 13. So before we begin simplifying our expression, we first need to recall the quotient rule of radicals which states that the square root of A divided by B is equivalent to the square root of A divided by the square root of B. So now just comparing our formula to our given expression, we can notice that the value of A is and that means the value of B is 1859. So now just utilizing this quotient rule formula, we can rewrite our given expression as the square root of 121 divided by the square root of 1859. So now we just want to start simplifying our expression. So first, we have the square root of 121 which we know simplifies to just 11. And now in the denominator, we want to break up the value of 1859 into its largest perfect square. So its largest perfect square is 169. So underneath the square root in the denominator, we have 169 multiplied by 11. And now we can continue to simplify. So again, we have 11 divided by and now the square root of 169 is 13. So in the denominator, we have 13 multiplied by the square root of 11. And now we see we have a radical in the denominator. So we want to simplify this expression by rationalizing the denominator. So we take our expression 11 divided by 13, multiplied by the square root of 11. And we need to multiply the numerator and the denominator by the square root of 11. So we have our expression multiplied by the square root of divided by the square root of 11. And now just simplifying in the numerator, we have 11 multiplied by the square root of 11. And in the denominator, we have 13 multiplied by 11. And now we can simplify this expression by noticing we have 11 in the numerator and in the denominator. So they cancel each other out and we are left with the simplified expression where we have the square root of 11 divided by 13. So with our simplified expression, we are left with answer choice C where again we have the expression, the square root of 11 divided by 13. 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. √4⁄50

Key Concepts

Product Rule for Radicals

Quotient Rule for Radicals

Simplifying Radicals

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