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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.$$\sqrt{18 b^{2}}+\sqrt{800 b^{2}}$$

23$\sqrt{2}|b|$

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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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all right, so in this exercise, we are going to be simplifying the expression 18 b squared, plus a radical 18 B squared plus radical 800 b squared. It's the first thing we want to do is find ways to break this down into a product of some number in a perfect square. So 18 is nine times to nine is a perfect square. We can factor it. Outside of the radical is three we're left with two and then b squared obviously is a perfect square sunken factor that outside of the radicals were left with three be radical too. Now 800 can be factored as two times 404 100 is a perfect square. It's 20 squared, obviously be squared is still a perfect square. So we're gonna rewrite that as 20 be radical tube. Now we can combine our coefficients on our radicals So three b plus 20 be simply 23 b radical too

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