Write the prime factorization of the following numbers and hence find their square roots.
(i) 7744
(ii) 9604
(iii) 5929
(iv) 7056.

To do:

We have to write the prime factorization of the given numbers and hence their square roots.

Solution: 

(i) Prime factorisation of 7744 is,

$7744=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 11 \times 11$

$=(2 \times 2 \times 2 \times 11)^2$

This implies,

$\sqrt{7744}=\sqrt{(2 \times 2 \times 2 \times 11)^2}$

$=(2 \times 2 \times 2 \times 11)$

$=88$

(ii) Prime factorisation of 9604 is,

$9604=2 \times 2 \times 7 \times7 \times 7 \times 7$

$=(2 \times 7 \times 7)^2$

This implies,

$\sqrt{9604}=\sqrt{(2 \times 7 \times 7)^2}$

$=(2 \times 7 \times 7)$

$=98$

(iii) Prime factorisation of 5929 is,

$5929=7 \times 7 \times 11 \times 11$

$=(7 \times 11)^2$

This implies,

$\sqrt{5929}=\sqrt{(7 \times 11)^2}$

$=(7 \times 11)$

$=77$

(iv) Prime factorisation of 7056 is,

$7056=2 \times 2 \times 2 \times 2\times 3 \times 3 \times 7\times7$

$=(2 \times 2 \times 3 \times 7)^2$

This implies,

$\sqrt{7056}=\sqrt{(2 \times 2\times 3\times 7)^2}$

$=(2 \times 2\times 3 \times 7)$

$=84$

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Updated on: 10-Oct-2022

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