Question

Using prime factorisation find the square root of 3364

Answer 1

3364 = 2×2×29×29
          = 2²×29²
          = 2×29
           58

Answer 2

$\begin{array}{r|l} 2 & 3364 \\ \cline{1-2} 2 & 1682 \\ \cline{1-2} 29 & 841 \\ \cline{1-2} 29 & 29\\ \cline{1-2} 1 & 1\end{array}$

Factors of 3364 = $\underbrace{2 \times 2} \times \underbrace{29 \times 29}$

$\sqrt{3364}$ = $\sqrt{2 \times 2 \times 29 \times 29}$

$\sqrt{3364}$ = 2 × 29

$\sqrt{3364}$ = 58

$\underline{\rm \therefore square\ root\ of\ 3364\ is\ 58}$

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Square root of a number is that number when multiplied by itself gives the original number .

It can also be said that a number when divided by its square root gives the divisor as a square root itself .

For example : Let the number be y which is equal to x² .

Hence , x is the square root of y .