(2sq root 5 + 3sq root 7)(2sq root 5 + 3sq root 7)
Using the distributive property:
(2sq root 5 + 3sq root 7)(2sq root 5 + 3sq root 7)
= 4(5) + 2(2sq root 5)(3sq root 7) + 2(2sq root 5)(3sq root 7) + 9(7)
= 20 + 12sq root 35 + 12sq root 35 + 63
= 83 + 24sq root 35
To simplify the expression (2√5 + 3√7)(2√5 + 3√7), you can use the distributive property.
First, distribute the terms:
(2√5)(2√5) + (2√5)(3√7) + (3√7)(2√5) + (3√7)(3√7)
Simplify each term:
4(√5)(√5) + 6(√5)(√7) + 6(√7)(√5) + 9(√7)(√7)
Remember that the square root of a number multiplied by itself gives the original number:
4(5) + 6(√5)(√7) + 6(√7)(√5) + 9(7)
Simplify the products inside the parentheses:
20 + 6(√35) + 6(√35) + 63
Combine like terms:
20 + 12(√35) + 63
Finally, simplify further:
83 + 12(√35)
So, the simplified expression is 83 + 12(√35).