Question

square root of 17424 by prime factorisation with method​

Answer 1

The prime factorisation of =>17424 = 2*2*2*2*3*3*11*11

= 2⁴*3²*11²

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Answer 2

$\bf \red{ \sqrt{17424} = 132}$

Given:

• $17424$

To find:

• Square root of number by prime factorization.

Solution:

Concept to be used:

• $\bf \sqrt[n]{ {a}^{n} } = a$

Step 1:

Find prime factors of number.

$2 |17424| \: \: \: \: \\ - - - - - \\ 2|8712| \: \: \: \: \: \: \\ - - - - - \\ 2|4356| \: \: \: \: \: \: \: \: \\ - - - - - \\ 2|2178| \: \: \: \: \: \: \: \\ - - - - - \\3 |1089| \: \: \: \: \: \: \: \: \\ - - - - - \\ 3 |363| \: \: \: \: \: \: \: \\ - - - - - \\ 11|121| \: \: \: \: \: \: \: \\ - - - - - \\11 |11| \: \: \: \: \: \: \: \: \: \: \\ - - - - - \\ |1| \: \: \: \: \: \: \: \: \: \: \: \:$

Thus,

Prime factors are

$\bf 17424 = {2}^{4} \times {3}^{2} \times {(11)}^{2}$

Step 2:

Find square root of 17424.

$\sqrt{17424} = \sqrt{ {2}^{4} \times {3}^{2} \times ( {11)}^{2} }$

or

$\sqrt{17424} = \sqrt{ {2}^{2} \times {2}^{2} \times {3}^{2} \times ( {11)}^{2} }$

or

$\sqrt{17424} = \sqrt{ {(2 \times 2 \times 3 \times 11)}^{2} }$

or

$\sqrt{17424} = 2 \times 2 \times 3 \times 11$

or

$\bf \sqrt{17424} = 132$

Thus,

Square root of 17424 is 132.

Learn more:

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