Question

find the square root of following numbers by the prime factorisation method ??

729,400,1764​

Answer 1

(i) 729

\sqrt{729}=\sqrt{3\times3\times3\times3\times3\times3}

729

=

3×3×3×3×3×3

= 3 x 3 x 3

= 27

(ii) 400

\sqrt{400}=\sqrt{2\times2\times2\times2\times5\times5}

400

=

2×2×2×2×5×5

= 2 x 2 x 5

= 20(iii) 1764

\sqrt{1764}=\sqrt{2\times2\times3\times3\times7\times7}

1764

=

2×2×3×3×7×7

= 2 x 3 x 7

= 42

Answer 2

Given :-

• Find the Square root of 729,400,1764.

Solutions:-

1) Square number 729 ??

LCM =

$3 |729 \\ 3 |243 \\ 3|81 \\ 3|27 \\ 3| 9 \\ 3 |3 \\ 1 \: is \: the \: last.$

We have pairs :-,

$\frac{3 \times 3}{} \times \frac{3 \times 3}{} \times \frac{3 \times 3}{} = 729$

$\sqrt{729} = 3 \times 3 \times 3 = 27$

••The Square root of the number 729 is 27

2), the square number 400 ??

LCM =

$2|400 \\ 2 |200 \\ 2|100 \\ 2|50 \\ 5|25 \\ 5 |5 \\ 1 \: is \: the \: last.$

So we have pairs :-

$\frac{2 \times 2}{} \times \frac{2 \times 2}{} \times \frac{5 \times 5}{} = 400$

$\sqrt{400 = } \: 2 \times 2 \times 5 = 20$

•The square root of the number 400 is 20

3) Square number 1764 ??

LCM =

$2 |1764 \ \\ 2|882 \\ 3 |441 \\ 3|147 \\ 7|49 \\ 7| 7 \\ 1is \: the \: last.$

So we have pairs :-

$\frac{2 \times 2}{} \times \frac{3 \times 3}{} \times \frac{7 \times 7}{} = 1764$

$\sqrt{1764} = 2 \times 3 \times 7 = 42$

•The Square root of the number 1764 is 42

Hope it is help you..

#,Be Brainly