Question

Find square root of 3969 by prime factorization

Answer 1

The square root of 3969 is 63. Prime factorisation is given below —

Answer 2

Answer:

Required square root is 63.

Step-by-step explanation:

Given number is 3969

Here we want to find square root of the given digit.

By prime factorisation, first we need to break 3969 into prime numbers.

$3969 = 3 \times 3 \times 3 \times 3 \times 7 \times 7$

Square root of 3969

$\sqrt{3969} \\ = \sqrt{3 \times 3 \times 3 \times 3 \times 7 \times 7} \\ = \sqrt{ {3}^{2} \times {3}^{2} \times {7}^{2} } \\ = {({3}^{2} \times {3}^{2} \times {7}^{2})}^{ \frac{1}{2} } \\ = 3 \times 3 \times 7 \\ = 63$

Square value list upto 30,

${1}^{2} = 1 \\ {2}^{2} = 4 \\ {3}^{2} = 9 \\ {4}^{2} = 16 \\ {5}^{2} = 25 \\ {6}^{2} = 36 \\ {7}^{2} = 49 \\ {8}^{2} = 64 \\ {9}^{2} = 81 \\ {10}^{2} = 100 \\ {11}^{2} = 121 \\ {12}^{2} = 144 \\ {13}^{2} = 169 \\ {14}^{2} = 196 \\ {15}^{2} = 225 \\ {16}^{2} = 256 \\ {17}^{2} = 289 \\ {18}^{2} = 324 \\ {19}^{2} = 361 \\ {20}^{2} = 400 \\ {21}^{2} = 441 \\ {22}^{2} = 484 \\ {23}^{2} = 529 \\ {24}^{2} = 576 \\ {25}^{2} = 625 \\ {27}^{2} = 729 \\ {28}^{2} = 784 \\ {29}^{2} = 841 \\ {30}^{2} = 900$