Question

(3√5 - √8) * (√8 + 3√5) +√48

Answer 1

$\tt \ \ \ (3\sqrt{5}-\sqrt{8})(\sqrt{8}+3\sqrt{5})+\sqrt{48}=(\sqrt{45}-\sqrt{8})(\sqrt{45}+\sqrt{8})+\sqrt{16\cdot3}=\\\\=(\sqrt{45})^2-(\sqrt{8})^2+4\sqrt{3}=45-8+4\sqrt{3}=37+4\sqrt{3}$

Answer 2

To simplify the expression (3√5 - √8) * (√8 + 3√5) + √48, we can start by multiplying the two binomials and then add the √48 term. Let's break it down step by step:

Step 1: Multiply the two binomials using the FOIL method (First, Outer, Inner, Last): (3√5 - √8) * (√8 + 3√5) = 3√5 * √8 + 3√5 * 3√5 - √8 * √8 - √8 * 3√5

Step 2: Simplify each term:

1. 3√5 * √8 = 3√(5 * 8) = 3√40
2. 3√5 * 3√5 = 3 * √(5 * 5) = 3 * √25 = 3 * 5 = 15
3. √8 * √8 = √(8 * 8) = √64 = 8
4. √8 * 3√5 = 3√(8 * 5) = 3√40

So, the expression becomes: 3√40 + 15 - 8 - 3√40 + √48

Step 3: Combine like terms: The terms "3√40" and "-3√40" cancel each other out: (3√40 - 3√40) + 15 - 8 + √48

Now, the expression becomes: 0 + 15 - 8 + √48

Step 4: Simplify further: 15 - 8 = 7

Finally, the expression is simplified to: 7 + √48

Step 5: Further simplify the square root of 48: √48 = √(16 * 3) = √16 * √3 = 4 * √3

So, the fully simplified expression is: 7 + 4√3