Chapter A.1, Problem 72E

Solution

Simplify the radical expression.

  $6\sqrt{7}$ .

Given:

The given expression is $2\sqrt{175}-2\sqrt{28}$ .

Concept Used:

• Find the largest factor in the radicand that is a perfect power of the index. Rewrite the radicand as a product of two factors, using that factor.
• Use the product rule to rewrite the radical as the product of two radicals.
• Simplify the root of the perfect power.

Calculation:

The given expression is $2\sqrt{175}-2\sqrt{28}$ .

  $\begin{array}{c}2\sqrt{175}-2\sqrt{28}=2\sqrt{5\cdot 5\cdot 7}-2\sqrt{2\cdot 2\cdot 7}\\ =2\sqrt{5^2\cdot 7}-2\sqrt{2^2\cdot 7}\\ =2\cdot 5\sqrt{7}-2\cdot 2\sqrt{7}\\ =10\sqrt{7}-4\sqrt{7}\\ =\sqrt{7}(10-4)\\ =6\sqrt{7}\end{array}$

Thus after simplifying $2\sqrt{175}-2\sqrt{28}$ we get $6\sqrt{7}$ .