Create and solve two problems involving addition, subtraction, multiplication and division of radicals the two problems combined should contain all four operations. For example problem 1 could contain addition and multiplication and the other problem division and subtraction
Problem 1:
First, simplify the following expression: (√12 + √3) * (√12 - √3)
Solution:
Using the difference of squares formula (a^2 - b^2 = (a + b)(a - b)), we can simplify the expression as follows:
(√12 + √3) * (√12 - √3)
= (√(4 * 3) + √3) * (√(4 * 3) - √3)
= (√4 * √3 + √3) * (√4 * √3 - √3)
= (2√3 + √3) * (2√3 - √3)
= (2 + 1) * (√3 * √3)
= 3 * √(3 * 3)
= 3 * √9
= 3 * 3
= 9
Therefore, (√12 + √3) * (√12 - √3) simplifies to 9.
Problem 2:
Calculate the following expression: (√25 + 4) ÷ (√9 - 2)
Solution:
Start by simplifying the numerator and denominator individually:
Numerator:
√25 + 4 = 5 + 4 = 9
Denominator:
√9 - 2 = 3 - 2 = 1
Now, substitute the simplified numerator and denominator back into the original expression:
(√25 + 4) ÷ (√9 - 2) = 9 ÷ 1 = 9
Therefore, (√25 + 4) ÷ (√9 - 2) equals 9.