ABC26GN1372 · Square Roots and Cube Roots
Subject: General Aptitude · Chapter: Square Roots and Cube Roots · Exam: 2010 · Marks: · Difficulty:
The number $25^{64} \times 64^{25}$ is the square of a natural number $n$. The sum of the digits of $n$ is
Answer
Explanation
$$\begin{aligned} & n^{2}=(25)^{64} \times(64)^{25}=\left(5^{2}\right)^{64} \times\left(2^{6}\right)^{25} \\ & \quad=5^{128} \times 2^{150}=5^{128} \times 2^{128} \times 2^{22} \\ & \Rightarrow n=5^{64} \times 2^{64} \times 2^{11}=(5 \times 2)^{64} \times 2^{11}=10^{64} \times 2048 . \\ & \therefore \text { Sum of digits of } n=2+0+4+8=14 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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