multiply (3√2 + 7)(3√2 + 5)
To simplify the expression, you can use the distributive property to expand the product:
(3√2 + 7)(3√2 + 5) = (3√2)(3√2) + (3√2)(5) + (7)(3√2) + (7)(5)
To multiply the terms with square roots, you can use the property √a * √b = √(ab).
= 9(2) + 15√2 + 21√2 + 35
= 18 + 36√2 + 35
= 53 + 36√2
Therefore, (3√2 + 7)(3√2 + 5) = 53 + 36√2.
To multiply (3√2 + 7)(3√2 + 5), you can use the distributive property. Start by multiplying the terms inside the parentheses:
(3√2 + 7)(3√2 + 5) = (3√2)(3√2) + (3√2)(5) + (7)(3√2) + (7)(5).
This simplifies to:
= (9 * 2) + (15√2) + (21√2) + (35).
Next, combine like terms:
= 18 + (15√2 + 21√2) + 35.
Simplify the terms with the square root:
= 18 + 36√2 + 35.
Finally, combine all the terms:
= 53 + 36√2.
So, (3√2 + 7)(3√2 + 5) simplifies to 53 + 36√2.
To multiply (3√2 + 7)(3√2 + 5), we can use the distributive property of multiplication.
Let's break it down step by step:
Step 1: Multiply the first terms in each parentheses.
(3√2)(3√2) = 3 * 3 * √2 * √2 = 9 * 2 = 18
Step 2: Multiply the outer terms in each parentheses.
(3√2)(5) = 3 * 5 * √2 = 15√2
Step 3: Multiply the inner terms in each parentheses.
(7)(3√2) = 7 * 3 * √2 = 21√2
Step 4: Multiply the last terms in each parentheses.
(7)(5) = 35
Step 5: Combine the like terms.
18 + 15√2 + 21√2 + 35 = 18 + 36√2 + 35 = 53 + 36√2
So, (3√2 + 7)(3√2 + 5) simplifies to 53 + 36√2.