What is the following product? (StartRoot 14 EndRoot minus StartRoot 3 EndRoot) (StartRoot 12 EndRoot + StartRoot 7 EndRoot) 2 StartRoot 42 EndRoot + 7 StartRoot 2 EndRoot minus 6 minus StartRoot 21 EndRoot StartRoot 14 EndRoot minus 6 + StartRoot 7 EndRoot StartRoot 26 Endroot + StartRoot 21 EndRoot minus StartRoot 15 EndRoot minus StartRoot 10 EndRoot 2 StartRoot 42 EndRoot minus StartRoot 21 EndRoot

Question:

What is the following product?

(√14 - √3) (√12 + √7)

Answer:

2√42 + 7√2 - 6 - √21

Step-by-step explanation:

Given.

(√14 - √3) (√12 + √7)

Required

Product

(√14 - √3) (√12 + √7)

We start by opening the brackets

√14 (√12 + √7) - √3 (√12 + √7)

√ (14*12) + √ (14*7) - √ (3*12) - √ (3*7)

Expand individual brackets

√ (2*7*2*6) + √ (2*7*7) - √ (3*3*4) - √ (3*7)

= √ (2*2*7*6) + √ (2*7*7) - √ (3*3*4) - √ (3*7)

= √ (4*42) + √ (2*49) - √ (9*4) - √ (3*7)

Split Roots as follows

= √4 * √42 + √2 * √49 - √9 * √4 - √21

Take square root of perfect squares

= 2 * √42 + √2 * 7 - 3 * 2 - √21

= 2√42 + 7√2 - 6 - √21

Hence, the result of the product (√14 - √3) (√12 + √7) is 2√42 + 7√2 - 6 - √21