Question

Which of the following is equivalent to 7 square root of 2 minus 3 square root of 8 plus square root of 18?

10 square root of 2


4 square root of 2


short dash 2 square root of 2


3 square root of 2

Answer 1

B) 4√2

Explanation:

Given expression:

`7 √(2)-3√(8)+√(18)`

Rewrite 8 as 4 · 2 and 18 as 9 · 2:

`\implies 7 √(2)-3√(4 \cdot 2)+√(9 \cdot 2)`

`\textsf{Apply radical rule} \quad √(ab)=√(a)√(b):`

`\implies 7 √(2)-3√(4) √(2)+√(9) √(2)`

Carry out √4 and √9:

`\implies 7 √(2)-3\cdot 2 √(2)+3 √(2)`

Multiply -3 and 2:

`\implies 7 √(2)-6 √(2)+3 √(2)`

Factor out √2:

`\implies (7 -6+3) √(2)`

Carry out the operations inside the parentheses:

`\implies 4√(2)`