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In $3-38$ write each expression in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.$$\sqrt{250 a^{2}}+\sqrt{10 a^{2}}$$

6$a \sqrt{10}$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 4

Adding and Subtracting Radicals

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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we're being asked to simplify the given expression. So remember, whenever you add radicals, you want to simplify all your radicals first. So let's start with our first radical. We have the square root of 250 a square. Well, 250 is not a perfect square, however, the perfect square 25 devise into it 10 times. So I'm going to rewrite it as two square with a 25 times to square the 10 and then I'll leave my a square than his own radical. Okay, so now let's take a look at the second radical. We have the square of the 10 A squared Well, we can simplify the square, the 10 fervor because no perfect square goes into 10 evenly. However, a squared is a perfect square to square. The H word is a so we can simplify this toe a times to square the 10. All right, let's go back to the first radicals and simplify well, the square, the 25 5, the square root of a square, this A and the square. The 10 can't be simplified, so I'll just bring that down. Then we'll bring down our second radical, a Britain. So now both radicals air simplified and these two radicals are Expressions are right terms because both radic cans of the same. So we just need to combine the coefficients well. Five a plus a is six a. So our final answer will be six a Times Square the 10.

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