Question

Simplify this expression.
$\\\\(\sqrt{2} + \sqrt{3})(\sqrt{5} - \sqrt{7} \\A: \sqrt{5} + \sqrt{-2} \\B: \sqrt{10} + \sqrt{15} - \sqrt{14} - \sqrt{21} \\C: 2\sqrt{5} - 2\sqrt{7} \\D: 2\sqrt{5} + 3\sqrt{5} - 2\sqrt{7} - 3\sqrt{7}$

Answer 1

By applying algebra, radical and power properties, we find that the simplified form of (√2 + √3) · (√5 - √7) is equal to √10 + √15 - √14 - √21. (Correct choice: B)

How to simplify a product of two binomials with radical numbers

Herein we need to apply algebra and radical and power properties to simplify the expression described in the statement, whose procedure is shown below:

1. (√2 + √3) · (√5 - √7)     Given
2. (√2 + √3) · √5 + (√2 + √3) · (- √7)     Distributive property
3. √2 · √5 + √3 · √5 + √2 · (- √7) + √3 · (- √7)     Distributive property
4. √10 + √15 - √14 - √21     (- a) · b = - a · b/ √a · √b = √a · b/Result

By applying algebra, radical and power properties, we find that the simplified form of (√2 + √3) · (√5 - √7) is equal to √10 + √15 - √14 - √21. (Correct choice: B)

To learn more on radical numbers: https://brainly.com/question/13184531

#SPJ1