Warm Up Solutions

Simplify.

$48 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 2^{4} \cdot 3$

$2^{\frac{4}{2}} 3^{\frac{1}{2}} 2^{2} \sqrt{3} 4 \sqrt{3}$

$(3 \cdot 4) (\sqrt{5 \cdot 7}) 12 \sqrt{35}$

Note

To simplify numbers completely, you must think in terms of their prime factorization.

Q: What are the coefficients of the radicals?

A: 3 and 4

Q: What are the two radicands?
A: 5 and 7

$\sqrt{(2 \cdot 5) (3 \cdot 5)} 5 \sqrt{6}$