Question

find the square root of 166464​

Answer 1

Answer :-.

• The square root of 166464 is 408.

To find :-

• The square root of 166464.

Solution :-

• Let's find the square root of 166464 by prime factorisation method!

Prime factorisation of 166464 :-

$\begin{array}{c | c} \sf\underline2 & \sf\underline{166464} \\ \sf\underline2 & \sf\underline{83232} \\ \sf\underline2 & \sf\underline{41616} \\ \sf\underline2& \sf\underline{20808} \\ \sf\underline{2}& \sf\underline{10404} \\ \sf\underline2 & \sf\underline{ \: \: 5202} \\ \sf\underline3& \sf\underline{ \: \: 2601} \\ \sf\underline3& \sf\underline{ \: \: \: 867} \\ \sf\underline{17}& \sf\underline{ \: \: \: 289} \\ \sf\underline{17}& \sf\underline{ \: \: \: \: 17} \\ & \sf{ \: \: \: \: \: \: 1} \end{array}$

We see that :-

• 166464 can be expressed as the product of pairs of equal prime factors. Hence it's a perfect square!

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Now :-

$\rm 166464 = \underbrace{2 \times 2} \times \underbrace{2 \times 2} \times\underbrace{2 \times 2} \times \underbrace{3 \times 3} \times \underbrace{17 \times 17}$

$\rm166464 = ({2}^{2}) \times ({2}^{2}) \times ({2}^{2}) \times ({3}^{2} ) \times ({17}^{2} )$

$\rm166464 = (2 \times 2 \times 2 \times 3 \times 17)^{2}$

$\rm166464 = (408)^{2}$

Hence :-

• The square root of 166464 is 408.

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Know more :-

What is square root of a number?

• The square root of a number is that number which when multiplied by itself gives that number as the product.