Algebra III - 6.5 Operations with Radical Expressions

Simplify  $\sqrt{36ab^4c^5}$  

•  $6b^2c^2\sqrt{ac}$  

•  $6ab^2c^2$  

•  $6b^2c^2$  

•  $6abc\sqrt{c}$  

Simplify  $\frac{\sqrt{c^5}}{\sqrt{d^9}}$  

•  $\frac{c^2\sqrt{cd}}{d^5}$  

•  $\frac{c^2}{d^4}$  

•  $\frac{c^2\sqrt{c}}{d^{4\sqrt{d}}}$  

•  $\frac{c}{d}\sqrt{\frac{c}{d}}$  

Simplify  $5\sqrt{2x}\times3\sqrt{8x}$  

•  $60x$  

•  $15\sqrt{40x^2}$  

•  $8\sqrt{40x^2}$  

•  $15\sqrt{16x}$  

Simplify  $5\sqrt{32}+\sqrt{27}+2\sqrt{75}$  

•  $20\sqrt{2}+13\sqrt{3}$  

•  $7\sqrt{100}$  

•  $8\sqrt{100}$  

•  $33\sqrt{5}$  

What is the process in which one eliminates radicals from the denominator or fractions from radicands.

• Rationalizing the denominator

• Conjugates

• The Principal Root

• Combining Like Expressions

Select all that are necessary when simplifying radicals

• The index must be as small as possible.

• The radicand contains no factors that are nth powers.

• The radicand contains no fractions

• No radicals appear in the denominator

Only _____________________________ can be combined when adding and subtracting radicals.

• Like radical expressions

• Unlike radical expressions

• radicals with the same index

• radicals with different indexes.

 $a\sqrt{b}+c\sqrt{d}\ and\ a\sqrt{b}-c\sqrt{d}$  are _________________. 

• Like radicals

• Conjugates

• Simplifed

• Principals

Simplify  $\left(4+2\sqrt{5}\right)\left(3\sqrt{3}+4\sqrt{5}\right)$  

•  $12\sqrt{3}+16\sqrt{5}+40+6\sqrt{15}$  

•  $12\sqrt{3}$  

•  $16\sqrt{5}$  

•  $40$  

Simplify  $\frac{8}{\sqrt{6}-5}$  

•  $\frac{\left(-40-8\sqrt{6}\right)}{19}$  

•  $\frac{27-10\sqrt{3}}{13}$  

•  $40$  

•  $-2-\sqrt{2}$