Question

(√5-2)^2+√60= ------------------------------------------------------------

Answer 1

$(\sqrt{5}-2)^2 +\sqrt{60} = 5 + 4\sqrt{5}+4+ 2\sqrt{15}=9+ 4\sqrt{5}+ 2\sqrt{15}$

Answer 2

To simplify the expression (√5-2)^2 + √60, follow these steps:

Step 1: Simplify the square of (√5-2)^2 First, square (√5-2)^2: (√5-2)^2 = (√5-2)(√5-2) = 5 - 4√5 + 4 Now the expression becomes: 5 - 4√5 + 4 + √60

Step 2: Simplify √60 √60 can be simplified by factoring 60 into its prime factors: 60 = 2 * 2 * 3 * 5 √60 = √(2 * 2 * 3 * 5) = √(2^2 * 3 * 5) = 2√(3 * 5) = 2√15

Step 3: Substitute √60 with 2√15 in the expression Now the expression becomes: 5 - 4√5 + 4 + 2√15

Step 4: Combine like terms Combine the constant terms (5 and 4): (5 + 4) = 9

Now the expression is: 9 - 4√5 + 2√15

So, (√5-2)^2 + √60 = 9 - 4√5 + 2√15.