Question:
What is the following product?
(√14 - √3) (√12 + √7)
Answer:
2√42 + 7√2 - 6 - √21
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