Question

find the positive square root of 16+ 2 root 55​

Answer 1

Answer: 30.8,323,969,741,913

Step-by-step explanation: Please mark me the brainleist

Answer 2

Answer:

Square root of ( 16 + 2√55 ) is (√11 + √5 ) .

Step-by-step explanation:

To find :

$\sqrt{(16 + 2 \sqrt{55}) }$

Solution :

• Let square root of ( 16 + 2√55 ) be (√a + √b ). Then,

$\sqrt{(16 + 2 \sqrt{55}) } = \sqrt{a} + \sqrt{b} \\ squaring \: both \: sides \: we \: get \\ 16 + 2 \sqrt{55} = ({ \sqrt{a} + \sqrt{b} })^{2} \\ 16 + 2 \sqrt{55} = a + b + 2 \sqrt{ab} \\ comparing \: both \: sides \: we \: get \\ a + b = 16 - - - (1) \\ ab = 55 \\ ⇒a = \frac{55}{b} - - - (2) \\ putting \: value \: of \: b \: from \: (2)in \: (1) \\ \frac{55}{b} + b = 16 \\ or \: \: \: \: {b}^{2} - 16b + 55 = 0 \\ {b}^{2} - 11b - 5b + 55 = 0 \\ (b - 11)( b- 5) = 0 \\ b= 11 \: or \: 5$

• Now, putting value of b in equation (2), we get

$a = \frac{b}{5} \\ if \: \: b = 11 \: then \: a = 5 \\ if \: b = 5 \: then \: a = 11$

• Hence, square root of ( 16 + 2√55 ) is (√11 + √5 )

$\sqrt{16 + 2 \sqrt{55} } = (\sqrt{11} + \sqrt{5} )$