Question

$\sqrt{248 + \sqrt{52 + \sqrt{144} } } \\ =$
​

Answer 1

Answer:

$\Large\boxed{16}$

Step-by-step explanation:

Given:

√248+√52+√144

$\Large\boxed{\textnormal{ESTIMATING (SOLVE) SQUARE ROOTS}}$

To solve this problem, first you have to estimating by the square root.

Solutions:

First, solve with square roots.

$\displaystyle \sqrt{52+\sqrt{144} }$

$12^2=12*12=144$

$\displaystyle \sqrt{12^2}$

Used radical rule.

$\Large\boxed{\textnormal{RADICAL RULES}}$

$\displaystyle \sqrt[N]{A^N}=A$

$\displaystyle \sqrt{12^2}=12$

Rewrite the problem down.

$\displaystyle \sqrt{52+12}$

Add.

$\displaystyle 52+12=64$

$\displaystyle \sqrt{64}$

Find the factor of 64.

$\displaystyle 8^2=8*8=64$

$\displaystyle \sqrt{8^2}$

$\displaystyle \sqrt{8^2}=8$

$\displaystyle \sqrt{248+8}$

Add.

$\displaystyle 248+8=256$

$\displaystyle \sqrt{256}$

$\displaystyle 16^2=16*16=256$

$\displaystyle \sqrt{16^2}$

Solve.

$\displaystyle \sqrt{16^2}=\boxed{16}$

$\large\boxed{16}$

Therefore, the correct answer is 16.