Question

Find the value of \[\sqrt {15612 + \sqrt {154 + \sqrt {225} } } \] is
A. 125
B. 13
C. 15
D. 25

Answer 1

Hint: In this question to find the square root of such a big number we will segregate the parts and find the individual square root . Use this to find the value of \[\sqrt {15612 + \sqrt {154 + \sqrt {225} } } \].

Complete step-by-step answer:
According to the question we have to find the value of \[\sqrt {15612 + \sqrt {154 + \sqrt {225} } } \] so for this we have to separate the parts means first find we will find the value of $\sqrt {225} $ then we will add the value in $\sqrt {154} $ then we will find there square root and then will add the value in $\sqrt {15612} $. So here we go
Hence
$
  \sqrt {225} = 15 \\
  \sqrt {154 + 15} = \sqrt {169} = 13 \\
  \sqrt {15612 + 13} = \sqrt {15625} = 125 \\
$
Hence the value of \[\sqrt {15612 + \sqrt {154 + \sqrt {225} } } \] is $125$.

Note: It is always advisable in such types of questions to follow the concept of square roots that a number which multiplied by itself to produce the original number .Remember squares of numbers from 1 to 15 it helps in the questions.