Question

If k = √(49 - 12√5), then find the value of k +2

Answer 1

Step-by-step explanation:

k = √(49 - 12√5)

= √(45 + 4 - 2 √180)

= √45 - √4

= 3 √5 - 2.

So, k + 2 = 3 √5 - 2 + 2 = 3 √5.

Answer 2

k + 2 = 3√5

Step-by-step explanation:

`\sf Given: k = \sqrt{49 - 12√(5) }`

`\sf \rightarrow k = \sqrt{49 - 12√(5) }`

step 1: breakdown

`\sf \rightarrow k = \sqrt{4 + 45- 2 * 2 * 3 √(5) }`

step 2: rewrite 45 = (3√5)²

`\sf \rightarrow k = \sqrt{4 + (3√(5))^2 - 2 * 2 * 3 √(5) }`

step 3: rearrange as per a² -2ab + b² = (a - b)²

`\sf \rightarrow k = \sqrt{ (3√(5))^2 - 2 * 3 √(5) * 2 +2^2}`

step 4: comparing, here: a = 3√5, b = 2

`\sf \rightarrow k = \sqrt{ (3√(5) -2)^2}`

step 5: simplify √a² = a

`\sf \rightarrow k = 3√(5) -2`

Then find k + 2

`\rightarrow \sf k = 3√(5) -2 + 2`

`\rightarrow \sf k = 3√(5)`