Question

Simplify. 1: if y>02: if y<0%5Csqrt%7B16y%5E2%7D" id="TexFormula1" title="1): -15\sqrt{y^2}\\2): -\sqrt{16y^2}" alt="1): -15\sqrt{y^2}\\2): -\sqrt{16y^2}" align="absmiddle" class="latex-formula">

Answer 1

In general, √(y²) = |y|, since y can be positive or negative and y² would have the same value either way.

So,

1) if y > 0, then |y| = y, and

-15√(y²) = -15 |y| = -15y

2) if y < 0, then |y| = -y, and

-√(16y²) = -|4y| = -|4| |y| = -4 (-y) = 4y