Question

Help me with this question please

Answer 1

`(991)/(40√(2))`

Explanation:

Given expression:

`√(72)-(48)/(√(50))-(45)/(√(128))+2√(98)`

Rewrite 72 as 36·2, 50 as 25·2, 128 as 64·2 and 98 as 49·2:

`\implies √(36 \cdot 2)-(48)/(√(25 \cdot 2))-(45)/(√(64 \cdot 2))+2√(49 \cdot 2)`

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

`\implies √(36)√(2)-(48)/(√(25)√(2))-(45)/(√(64)√( 2))+2√(49)√(2)`

Rewrite 36 as 6², 25 as 5², 64 as 8² and 49 as 7²:

`\implies √(6^2)√(2)-(48)/(√(5^2)√(2))-(45)/(√(8^2)√( 2))+2√(7^2)√(2)`

`\textsf{Apply radical rule} \quad √(a^2)=a, \quad a \geq 0`

`\implies 6√(2)-(48)/(5√(2))-(45)/(8√( 2))+2\cdot 7√(2)`

Simplify:

`\implies 6√(2)-(48)/(5√(2))-(45)/(8√( 2))+14√(2)`

Combine like terms:

`\implies 20√(2)-(48)/(5√(2))-(45)/(8√( 2))`

Make the denominators of the two fractions the same:

`\implies 20√(2)-(384)/(40√(2))-(225)/(40√( 2))`

Rewrite 20√2 as a fraction with denominator 40√2:

`\implies 20√(2)\cdot(40√(2))/(40√(2))-(384)/(40√(2))-(225)/(40√( 2))`

`\implies (1600)/(40√(2))-(384)/(40√(2))-(225)/(40√( 2))`

Combine fractions:

`\implies (991)/(40√(2))`