Question

find the square root of 4096 by prime factorization method

Answer 1

Square root of 4096
4096=2×2×2×2×2×2×2×2×2×2×2×2=64
Hope it helped you

Answer 2

$\large{\boxed{\boxed{\boxed{\bold{\green{Solution :}}}}}}$

2 | 4096
2 | 2048
2 | 1024
2 | 512
2 | 256
2 | 128
2 | 64
2 | 32
2 | 16
2 | 8
2 | 4
2 | 2
....| 1

Now,

$\bold{4096 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times} \\ \bold{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2 \times 2 \times 2 \times 2 \times 2} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \bold{= {2}^{2} \times {2}^{2} \times {2}^{2} \times {2}^{2} \times {2}^{2} \times {2}^{2} }$

$\bold{ \sqrt{4096} = \sqrt{2 {}^{2} } \times {2}^{2} \times {2}^{2} \times {2}^{2} \times {2}^{2} \times {2}^{2}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{= 2 \times 2 \times 2 \times 2 \times 2 \times 2} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{= 64}$