Answer:
B) 4√2
Step-by-step explanation:
Given expression:
[tex]7 \sqrt{2}-3\sqrt{8}+\sqrt{18}[/tex]
Rewrite 8 as 4 · 2 and 18 as 9 · 2:
[tex]\implies 7 \sqrt{2}-3\sqrt{4 \cdot 2}+\sqrt{9 \cdot 2}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies 7 \sqrt{2}-3\sqrt{4} \sqrt{2}+\sqrt{9} \sqrt{2}[/tex]
Carry out √4 and √9:
[tex]\implies 7 \sqrt{2}-3\cdot 2 \sqrt{2}+3 \sqrt{2}[/tex]
Multiply -3 and 2:
[tex]\implies 7 \sqrt{2}-6 \sqrt{2}+3 \sqrt{2}[/tex]
Factor out √2:
[tex]\implies (7 -6+3) \sqrt{2}[/tex]
Carry out the operations inside the parentheses:
[tex]\implies 4\sqrt{2}[/tex]
