Question

What is the simplified form (3 + √3) ( 5+ √3 )

Answer 1

The simplified form of (3 + √3) ( 5+ √3 ) is 18 + 8√3, which is found by distributing the terms and combining like terms.

Step-by-step explanation:

To find the simplified form of (3 + √3) ( 5+ √3 ), we will use the distributive property, also known as the FOIL method in algebra for binomials. Here's the step-by-step simplification:

1. Multiply the first terms: 3 × 5 = 15.
2. Multiply the outer terms: 3 × √3 = 3√3.
3. Multiply the inner terms: √3 × 5 = 5√3.
4. Multiply the last terms: √3 × √3 = 3, since √x² = √x.
5. Add all the products together: 15 + 3√3 + 5√3 + 3.
6. Combine like terms: 15 + 3 + (3√3 + 5√3) = 18 + 8√3.

Therefore, the simplified form of (3 + √3) ( 5+ √3 ) is 18 + 8√3.