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What is the square root of $105464$ ?

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114

1012

1014

10014

answer is C.

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Detailed Solution

The given number is

105464

.
For any real number,

a 2 = a

.
Rewrite the given expression as,

⇒ 105464 = 672464

Prime factorize both the numerator and denominator,

⇒ 672464 = 2 × 2 × 41 × 41 2 × 2 × 2 × 2 × 2 × 2 ⇒ 22 × 412 22 × 22 × 22

Finding the square root,

⇒ 105464

= 672464

⇒ 22 × 412 22 × 22 × 22

⇒ 2 × 41 2 × 2 × 2

⇒ 414

⇒ 1014

Hence, the square root of

105464 = 1014

.
Therefore, option 3 is correct.

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