Question

Find The value Of:
$\sqrt{46 + \sqrt{5 + \sqrt{4 + \sqrt{144} } } }$
​

Answer 1

Answer:

$\sqrt{46 + \sqrt{5 + \sqrt{4 + \sqrt{144} } } }$

$\sqrt{46 + \sqrt{5 + \sqrt{4 + \sqrt{12 \times 12} } } }$

$\sqrt{46 + \sqrt{5 + \sqrt{4 + 12} } }$

$\sqrt{46 + \sqrt{5 + \sqrt{16} } }$

$\sqrt{46 + \sqrt{5 + \sqrt{4 \times 4} } }$

$\sqrt{46 + \sqrt{5 + 4} }$

$\sqrt{46 + \sqrt{9} }$

$\sqrt{46 + \sqrt{3 \times 3} }$

$\sqrt{46 + 3}$

$\sqrt{49}$

$\sqrt{7 \times 7}$

$7$

Ans. 7

Hope it helps.

Answer 2

• We have to evaluate the above expression by using the given data.

              Given data:- $\sqrt{46+\sqrt{5+\sqrt{4+\sqrt{144}}}}.$

              To find:- Value of above expression.

              Solution:-

• To solve the above equation we will follow the BODMAS rule.

• BODMAS is an order of mathematic operations.

• BODMAS rule is to be followed while solving expressions in mathematics. It stands for,

      B= bracket

      O= order of power or rules

      D= division

      M= multiplication

      A= addition

      S=subtraction

     Therefore,

$\begin{array}{l}=>\sqrt{46+\sqrt{5+\sqrt{4+\sqrt{144}}}} \\=>\sqrt{46+\sqrt{5+\sqrt{4+\sqrt{12 \times 12}}}} \\=>\sqrt{46+\sqrt{5+\sqrt{4+12}}} \\=>\sqrt{46+\sqrt{5+\sqrt{16}}} \\=>\sqrt{46+\sqrt{5+\sqrt{4 \times 4}}} \\=>\sqrt{46+\sqrt{9}} \\=>\sqrt{46+\sqrt{3 \times 3}} \\=>\sqrt{46+3} \\=>\sqrt{49} \\=>\sqrt{7 \times 7} \\=>7.\end{array}$

 Hence we will get the value $\sqrt{46+\sqrt{5+\sqrt{4+\sqrt{144}}}}=7.$