Question

PLEASEEEEE

Match the expressions with their simplified versions.

Answer 1

Answer:

1. $\normalsize \boxed{\textsf{ 4\sqrt{2}\cdot\sqrt{2} }} \implies \boxed{8}$

2. $\normalsize \boxed{\textsf{ 3\sqrt{7}-2\sqrt{7} }} \implies \normalsize \boxed{\textsf{ \sqrt{7} }}$

3. $\normalsize \boxed{\textsf{ \dfrac{\sqrt{7}}{2\sqrt{7}} }} \implies \normalsize \boxed{\textsf{ \dfrac{1}{2} }}$

4. $\normalsize \boxed{\textsf{ 2\sqrt{5}\cdot 2\sqrt{5} }} \implies \boxed{20}$

Step-by-step explanation:

The Radical Rules by Lial et al. (2017) state that:

Product rule: $\large \textsf{ \sqrt[n]{a}\cdot\sqrt[n]{b}=\sqrt[n]{ab} }$

• "The product of two roots is the root of the product."

Quotient rule: $\large \textsf{ \sqrt[n]{\dfrac{a}{b}}=\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}} }\ \ \textsf{ (b \neq 0) }$

• "The root of a quotient is the quotient of the roots."

1.

$\implies \normalsize \textsf{ 4\sqrt{2}\cdot\sqrt{2} }\\\\\normalsize \implies \textsf{ 4\sqrt{2\cdot2} }\\\\ \implies \normalsize \textsf{ 4\sqrt{4} }\\\\ \implies\normalsize \textsf{ 4\cdot 2 = 8 }$

$\normalsize \boxed{\textsf{ 4\sqrt{2}\cdot\sqrt{2} }} \implies \boxed{8}$

2.

$\implies \normalsize \textsf{ 3\sqrt{7}-2\sqrt{7} }\\\\ \implies\normalsize \textsf{ (3-2)\sqrt{7} }\\\\ \implies\normalsize \textsf{ 1\sqrt{7} }\\\\ \implies\normalsize \textsf{ \sqrt{7} }$

$\normalsize \boxed{\textsf{ 3\sqrt{7}-2\sqrt{7} }} \implies \normalsize \boxed{\textsf{ \sqrt{7} }}$

3.

$\implies \normalsize \textsf{ \dfrac{\sqrt{7}}{2\sqrt{7}} }\\\\\\ \implies\normalsize \textsf{ \dfrac{1\sqrt{7}}{2\sqrt{7}} }\\\\\\ \implies\normalsize \textsf{ \dfrac{1}{2} }$

$\normalsize \boxed{\textsf{ \dfrac{\sqrt{7}}{2\sqrt{7}} }} \implies \normalsize \boxed{\textsf{ \dfrac{1}{2} }}$

4.

$\implies \normalsize \textsf{ 2\sqrt{5}\cdot 2\sqrt{5} }\\\\ \implies\normalsize \textsf{ 2\cdot2\sqrt{5\cdot5} }\\\\ \implies \normalsize \textsf{ 4\sqrt{25} }\\\\ \implies \normalsize \textsf{ 4\cdot5=20 }$

$\normalsize \boxed{\textsf{ 2\sqrt{5}\cdot 2\sqrt{5} }} \implies \boxed{20}$

Reference:

Lial, M., Hornsby, J., Schneider, D., & Daniels, C. (2017). College Algebra and Trigonometry, Global Edition (6th ed., p. 94).