Question

How do you evaluate `(2\sqrt { 2} + 5) ( \sqrt { 10} - 3)`?

Answer 1

Approximately `1.2704`

Explanation:

Now, remember that:
`(a+b)(c+d)=ac+ad+bc+bd`

Therefore, `(2sqrt2+5)(sqrt10-3)` is equal to `2sqrt2*sqrt10+(-3*2sqrt2)+5sqrt10-15` Now, remember that: `sqrta*sqrtb=sqrt(ab)`

Therefore, we can simplify `2sqrt2*sqrt10+(-3*2sqrt2)+5sqrt10-15`.

=>`2sqrt2*sqrt10+(-3*2sqrt2)+5sqrt10-15`

=>`2sqrt20-6sqrt2+5sqrt10-15` Now, remember that: `sqrt (a^2*b)=asqrtb`

=>`4sqrt5-6sqrt2+5sqrt10-15`

=>`-6sqrt2+4sqrt5+5sqrt10-15` which is approximately `1.2704`