Question

step by step answer
$\sqrt{248 + \sqrt{52 + \sqrt{144} } }$
​

Answer 1

Answer:

We need to find value of   √248 +  52 +  144

​ ​  =  √248 +  52 + 12

​=  √248 +  64

​ =  √248 + 8

​ =  √256

​ = 16

Hope it helps you!!

Answer 2

ANSWER:

To Simplify:

• $\sqrt{248 + \sqrt{52 + \sqrt{144} } }$

Solution:

We are given that,

$\implies \sqrt{248 + \sqrt{52 + \sqrt{144} } }$

We know that,

⇒ 144 = 12 × 12

$\implies \sqrt{248 + \sqrt{52 + \sqrt{12\times12} } }$

$\implies \sqrt{248 + \sqrt{52 + \sqrt{12^2} } }$

$\implies \sqrt{248 + \sqrt{52 + 12 } }$

$\implies \sqrt{248 + \sqrt{64 } }$

We know that,

⇒ 64 = 8 × 8

$\implies \sqrt{248 + \sqrt{8\times8 } }$

$\implies \sqrt{248 + \sqrt{8^2 } }$

$\implies \sqrt{248 + 8 }$

$\implies \sqrt{256}$

We know that,

⇒ 256 = 16 × 16

$\implies \sqrt{16\times16}$

$\implies \sqrt{16^2}$

$\implies 16$

Therefore,

$\implies\bf \sqrt{248 + \sqrt{52 + \sqrt{144} } }=16$