Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4 - Page 418: 17

$40 \sqrt{6}$

Work Step by Step

First of all, in order to make this one large square root, we multiply the coefficients to obtain that the new coefficient is 20. Also, recall, $\sqrt{a}\times \sqrt{b}= \sqrt{a \times b}$. Thus, we can multiply 2 and 12 to obtain the simplified expression: $20\sqrt{2 \times 12}=20\sqrt{24}$ In order to simplify a radical, we consider the factors of the number inside of the radical. If any of these factors are perfect squares, meaning that their square root is a whole number, then we can simplify the radical. We know that 6 and 4 are factors of 24. We know that 4 is a perfect square, so we simplify: $20 \sqrt{4} \sqrt{6}=40 \sqrt{6}$

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