Question

learn multiplying radical expressions
multiplying radical expressions is similar to multiplying rational numbers.
to multiply radical expressions, multiply the coefficients and multiply
the radicands. this is similar to the way rational numbers are multiplied
by multiplying the numerators and multiplying the denominators.
rational numbers
$\frac{5}{3} cdot \frac{2}{7} = \frac{5 cdot 2}{3 cdot 7}$
$= \frac{10}{21}$
radical expressions
$5sqrt{3} cdot 2sqrt{7} = (5 cdot 2)sqrt{3 cdot 7}$
$= 10sqrt{21}$
example 4 multiply radical expressions
simplify $5sqrt{3} cdot 4sqrt{6}$.
$5sqrt{3} cdot 4sqrt{6} = (5 cdot 4)(sqrt{3} cdot sqrt{6})$
$= $
$= 20(3sqrt{2})$
$= $
check
simplify $3sqrt{10} cdot (-9sqrt{6})$.

Explanation:

Step1: Solve Example 4 Step1

Multiply coefficients and radicands:
$5\sqrt{3} \cdot 4\sqrt{6} = (5 \cdot 4)(\sqrt{3 \cdot 6}) = 20\sqrt{18}$

Step2: Simplify $\sqrt{18}$

Factor radicand into perfect square:
$\sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2}$
So the expression becomes $20(3\sqrt{2})$

Step3: Solve Example 4 Step3

Multiply the coefficients:
$20 \times 3\sqrt{2} = 60\sqrt{2}$

Step4: Solve the Check problem Step1

Multiply coefficients and radicands:
$3\sqrt{10} \cdot (-9\sqrt{6}) = (3 \cdot -9)(\sqrt{10 \cdot 6}) = -27\sqrt{60}$

Step5: Simplify $\sqrt{60}$

Factor radicand into perfect square:
$\sqrt{60} = \sqrt{4 \cdot 15} = 2\sqrt{15}$

Step6: Finalize Check problem

Multiply the coefficients:
$-27 \times 2\sqrt{15} = -54\sqrt{15}$

Answer:

Example 4 blanks:

1. $20\sqrt{18}$
2. $60\sqrt{2}$

Check problem answer:
$-54\sqrt{15}$